In Beijing speech 找碴儿 means 'to pick a fight / nitpick' - literally 'looking for a sharp edge to grab onto'. The image of jagged glass shards underlies the slang meaning of grudges and quarrels.
Stone radical on the left, the indexing radical. 碴 means a sharp fragment or shard - broken glass, chipped pottery, beard stubble - all hard, splinter-like things. The radical groups it with 砖 brick, 碎 to smash, 砸 to crush, all hard-material chars.
Right side 查 supplies the sound - chá straight across with no shift. There is a faint sense of inspecting that fits the imagery of finding a sharp shard. Same phonetic appears in 楂 hawthorn and 渣 dregs.
