If they liked being with him, then why would they try to escape all the time?
The only beasts that escaped had a specific reason for leaving the suitcase.
(Almost) all of the beasts had a specific reason for leaving. Let's go through the list:
This animal loves shiny things, and can't get enough of them. We see what Hagrid says:
"These're nifflers," said Hagrid, when the class had gathered around. "Yeh find 'em down mines mostly. They like sparkly stuff... There yeh go, look."
Harry Potter and the Goblet of Fire, chapter 28
He only went out to collect more shiny stuff.
This beast jumps out and attacks Jacob when he opens Newt's monstrous suitcase. It's only defending itself!
This is the rhino-like thingy. It was in heat - it was looking for a mate. That's why Jacob got in such big trouble when he gets doused with the pheromones.
This is the blue snake-like animal.
You'll recall that the egg fell out of Newt's pocket - apparently this hatched out of it, so technically this was never in the suitcase.
This is the invisible creature, whose hair can be woven into Invisibility Cloaks.
Newt states why this one escaped - he learned from Newt, and was looking after the Occamy.
This the blue bug. I'm not quite sure why it escaped. But it's a bug, and you know that bugs go everywhere...
This was just following Newt around, as he really really liked him :P. It wasn't trying to get away.
Newt may have originally captured them against their will, as they were wild animals, but they were tamed. The only ones that escaped did so not because they felt imprisoned, but for other reasons.
All images taken from the Harry Potter Wiki.