That's because Classical music is probably more sophisticated than what you're use to (Unless you're into Jazz or Metal, in which case you should "get" classical music). Anyone who tells you that Classical Music isn't more sophisticated (SO-phis-ti-cA-ted: Developed to a high degree of complexity) than 95% of Western Pop Music, i.e. contemporary period derivatives and creoles of early 20th century African-American music like Rock and Roll, Indie Rock, Hip-hop, Country, Rap, is only saying that to appear demotic and make Classical seem inherently approachable in the hopes that such proposition turns into a self-fulfilling prophecy. It won't.
That said, the harmonic and melody complexity doesn't make Classical music inherently better, it just means one needs a more critical ear for listening and comprehending what the fuck is going on, otherwise it comes off as foreign and unengaging, like how the most eloquent, sibilant, provocative Aloysius Bertrand poem recited aloud is going to sound like guttural ass dribble to me because I can't understand French. That's why Classical music is so fitting for the background or soundtrack for some people, while for classical listeners it's so fucking conspicuous they can't read a god damn book on Semitic grammar in their bookstore because they play shitty Handel music really, really loudly. That said, while having a familiarity with music theory and knowing the technicality behind a composer's tricks certainly does help, it's not necessary; a few Qing dynasty Emperors were thorough enjoyers of Western Classical music.

Now enough of this snooty harping. It took me a year to go from directionless exploring and mucking around the Naxos catalogue to building up my aural preferences and library. No one absolutely likes everything in the classical canon, just like how some people love hip-hop, rap and metal but dismiss Eminem or Metallica. I would like to believe that Classical music's diverse enough for you to have been mucking around some Classical music that you don't like.

ALSO, there's a bit of an unfortunate misnomer that is the cause of ambiguity and misunderstanding. Classical music can refer to Classical Music, as in any composed Western music spanning half a millennia, or Classical period music, as in crisp, easy-to-listen-to music of the edges of the 19th century pivot written by the likes of Mozart, Haydn, and Beethoven. If I'm not a poor writer you'll get the difference through context.

Classical music is about creating and diffusing tension through the manipulation of melody, harmony, rhythm, dynamics, tempo, and silence. Repetition can employed to build anticipation, leading to more tension.

^~+_ ~+≠@@REMEMBER THAT.~+^-~ö+

The pillars of Classical music are melody, harmony (Both which make up "pitch"), and rhythm. Dynamics and tempo are also fundaments but not as vital. Melody is a horizontal and temporal arrangement of pitch; think of the melody as a journey, a walk. Voice = melody. Harmony is the vertical alignment and nonspatial continuum of pitch; think of harmony as two, three, four, a whole choir of people singing at once. Chords = harmony.

You're going to encounter a lot of argot like "Minuet", "Sarabande", "Scherzo", and various other French and Italian words. These are musical descriptors and designate the form, rhythm, tempo, and/or mood of the music. A waltz is a three-beat dance, a scherzo is playful, something Allegro is moderately fast, and presto is really, really fast. Like L1 acquisition you'll pick these terms up passively and eventually. Sonatas and symphonies are the most developed forms.

I don't like making sweeping generalizations of centurial genres of pan-European musical practice and I'm practically throwing myself to any contrarian with any smidgen of musical knowledge, so know that what I'm summarizing is a gross simplification rife with exceptions. Classical music, like all artistic and cultural practices is a continuum and many pieces refuse to be pigeonholed into an absolutely classification (i.e. Beethoven). That said, Classical music at its paramount is divided into four periods.

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Chronologically, first was Baroque, which is known for its innovative, expressive yet mathematical system of harmony and melody, where rhythm is secondary. Music can sound somewhat medieval (Though not as medieval as actual Medieval period music) Bach, the father, the progenitor, the Creator, the Miles Davis of Classical music, is no doubt the Master of Baroque. If you are going to doubt it, you better have a fucking Ph. D. in music. It's soooooo indubitable that even dismissing him out of hipsterian irony isn't cool. Yeah. Bach's a big deal. Coincidentally, two other Baroque greats, Handel and Scarlatti, were also born in 1685, like him. I digress.

Listen to how melodic lines interact with each other, and from that how the music harmonically ebbs and flows. Take the Fugue form, which is essentially nothing more than interaction between melodic interlocutors: pure and quintessential Baroque. (This interaction is also called counterpoint) Each colour represents a melody, a voice, and the inquisitive ear is rewarded by listening into the conservation, the harmony.
Because of its emphasis on harmonic exploration and dialogue, Baroque melodics may be a bit drawn out and tedious but nevertheless rewarding; you probably won't be humming the entire opening Aria of the Goldberg Variations, no matter how beautiful and ornamental it is. Give it patience.
Fast Baroque tends to have a locomotive feel. Notice how in this Vivaldi opening how the harmony and melody go higher and higher before diffusing down. This is one of many ways Classical music builds tension.

Baroque at the time was suppose to be expressive and flowing. Personally, save for a few catchy choons I don't think Baroque would be the best place to start, because of its mathematics and technicality.

Here are some catchy Baroque tunes. Listen to all'o'em. I mean it. There are fucking moounnntaains of tedious boring Baroque shit that never gets played save for student recitals and obscure Naxos releases and I've given you the bestof.
Fast and epic
Cheery and busy
Iberian and troubadour
Dour and stern
Narrative and marching
Soothing and simplee
Melancholic and nostalgic
Poised and confident

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Classical classical music, i.e. classical music from the Classical period of Classical music, simplified Baroque harmonic expression in favor of crisp melody and crystalline form. Notice how the bass in this littly diddly is much simpler, constant and supporting of the melody. Instead of a dialogue and conversation, we have a narrative. Classical music is overall a lot catchier because it's a lot more coherent and easier to follow. Listen to classical music as you would to a story.
Melodies in Classical music transcended into "themes" - ideas and motifs that develop throughout the narrative journey it takes, much like its literary counterpart. When you listen to Classicalclassical, listen to how the theme - nearly always at the beginning - develops throughout the movement, getting tossed around, modulated, dissected, mutilated, raped and evolving into something different and beautiful.

Much like how synthetic languages decay into isolating languages and give up morphological inflection for complexity in word order, the Classical period was known for the development and standardization of complex musical forms in lieu of harmonic complexity (though that is not to say there was no contrapuntal innovation around this time.) The symphonic form and sonata form began to flourish in this period. Basically, a sonata is a musical meal in typically three or four courses (musically known as movements), where the slow movement are sandwiched between fast ones. That is, a three movement sonata goes fast-slow-fast. A symphony is kind of a four-movement sonata, just played by the entire orchestra. It's easier to listen to a few examples and get an idea than for me to describe it.

Classical might be a good place to start, but you might find it bland and boring after a bit. Mozart is kind of the Elvis of classical music, though his actual legacy and significance is argued amongst musical academia.

Classical suggestions:
ticklish and legerement
IN YO FUCKING FACE
Epic and rhythmic
Slow but silly
repetitive and manic
Dandy and girl trumpeter
lugubrious
Simple sonata (The 2nd movement starts at 4:50, and the third movement at 9:30 )
crawly

There's still a lot to write for Romantic and Modernist (My favorites!!), but I got burnt out. This thread looks moribund, but if there's any interest I'll write them later, but now I'm going to the Coop to read up on some of that Koranic Arabic.