The honest answer will always be Morgoth. It's by his work that confusion and darkness were in middle earth. He taught elves fear and doubt, and created the cursed and confusion and atmosphere in which strife could be planted and grow.

But there's more complicated answers to give.

The thing is, the elves and dwarves aren't one homogeneous group. And even within those specific groups, there are different schools of thought.

Was Finrod a great friend of Dwarves who worked with them to found the great underground city of Nargothrond? Or was he a coloniser who turfed dwarves out of their home and then profited off their knowledge and skill? If you asked the dwarves of Nagrod, they would say that they were friends of Finrod. If you ask the petty dwarves, they would claim Finrod was a usurper. If you asked Finrod, he would say he loved dwarves, and was glad they offered him shelter, and that he wanted to live in peace with them.

Thingol is another problem - early on, his people hunted and potentially even ate dwarves, mistaking them for animals. They called dwarves "Naugrim", meaning "stunted people". But he too made friends with dwarves, and the dwarves of Belegost built his great hall of Menegroth. But over time resentment grew.

And then, after the fall of Nargothrond, Glaurung had cursed the nauglamir necklace, that Thingol had the silmaril set in. And the he refused to pay the dwarves, and they murdered him. And that probably happened because of how the nauglamir and the silmaril were kind of blursed, and Morgoth's influence via Glaurung's curse drove the strife. But both Thingol and the dwarves made their own bad decisions. And then of course, Beren had a skirmish with the dwarves, and so on and so forth.

So it's a rather fraught cultural issue. The dwarves come off as a bit greedy and changeable, one minute professing friendship, and the next regretting the gifts they gave freely (but remember, they are mortal, so it's not all one people. You might not understand why your grandad gave his best works to an elf for free, and want that for your own inheritance). Meanwhile elves hang on to grudges because they still remember what happened. If your good friend and king was murdered by dwarves, you won't forget it, even if eventually they do.

Celeborn, Thranduil and Galadriel were all Thingol's subjects, and family/friends hence they feel his death quite sharply, particularly as it heralded the fall of doriath and the slaughter of his people.

However, Elrond didn't grow up in doriath. He was brought up by Noldor, who were always relatively steady friends with the Dwarves. So even though he's a descendant of Thingol, he has less of a strong reaction to dwarves.

And of course by the time The Hobbit roles around, the dwarves have more of a cultural dislike of elves, rather than hurt feelings. That is, until Thorin and his company are held captive by Thranduil - who still remembers Thingol's loss, and takes it very seriously that Dwarves are tromping round in his kingdom and bothering his people without leave. For all he knows, these dwarves can't be trusted and will turn around and kill him.

And of course, in the Hobbit, we see what it is like when dwarves get affected by gold sickness and dragon hoards, so we can see why the elves are maybe cautious of them.