Rick has no problem bailing on Beth and Summer (including leaving them to die) even though we've seen plenty of times that he cares about them in their own rights.But he always takes Morty with him when skipping dimensions and hates the idea of something bad happening to him when it's very easy to get a new Morty.Rick is a complete bastard, yet this Morty is special to him. Why? My theory is that our Morty is the only person left from Rick's original dimension , that's why he's so protective of him.
Given that in current dimension he's occupying Rick's been gone for longer than Morty's been alive and yet he has memories of Morty as a baby, I think for whatever reason he left his baby grandson in a different dimension, most likely where lil Morty died unnoticed, and then went to live somewhere else.There was apparently a cut scene where little Summer noticed Rick sneaking into Morty's crib and went to alarm her parents- it's a possible moment when this switch could've happened.Then, before the first episode Rick decided to go live in a dimension where he left his real grandson in. Him being responsible for Evil Morty being the way he is could still work- he would just be one of many Mortys Rick lived with for 14 years before the first episode, instead of the Rick's original.
I know it is pretty complicated, but Rick has plenty of complicated things about him XD