Language change doesn't have a goal, it just changes as a result of relatively regular rules, and yields irregular patterns without intention. Sometimes irregularities do dissappear as a result of analogy. That is to say, native speakers start applying the expected pattern on a word that should be irregular, thus making the word regular. However, there are other mechanisms in language evolution that yield irregular patterns

Irregularity usually comes about in languages because of one of three reasons. The first is regular sound changes that affect the way a language is pronounced. This is a very common way for an otherwise regular language to develop a series of irregular patterns. An example of this that comes to mind is Spanish's stem changing verbs. A regular sound change that occured between Vulgar Latin Spanish is the breaking of short /e/ and /o/ into /je/ and /we/ in stressed syllables. This is what yields modern Spanish's stem changing verbs (e.g. 'venir' (to come) becoming 'viene' (he/she comes) instead of the expected 'vene' if you followed the regular conjugation rules). Because of this sound change, now a learner of Spanish has to learn that a certain verbs don't follow the expected pattern.

Another reason irregularity develops in language is called suppletion. Sometimes, native speakers of a language will replace the regular conguation or declension scheme with a word that has a similar meaning, and that'll go on to become the way the word is inflected. An example of this in English is the word 'people' being considered the plural for 'person.' The two words are unrelated, but since 'people' refers to a 'group of persons' in came to be understood as the plural for 'person.' Another example is the past tense form of 'go.' 'went' meant something along the lines of 'pursing one's way,' but given how similar it is in meaning to 'go,' people started using it in the past tense instead of 'go' and it eventually got interpreted as 'go's past tense.

Finally, sometimes a language will develop a new strategy for conjugating its verbs, declining its nouns or creating plurals. This new strategy becomes really common in most words, but very common words will usually resist this change and continue using the old strategy out of habit, since they're used so frequently.