Cole had cause when Kendrick said “Mutha fukk the big 3/ its just big ME!”. Yes the rest of his Like That verse was aimed squarely at Drake but the big 3 line was Cole’s line and Kendrick said he was the best and thats enough to engage in a battle if Cole really felt like lacing em up.
We all know what happened afterwards so no need to rehash but Cole, as an MC , was well within his rights to take offense as a RAPPER and challenge Dot. 7 Minute Drill was just that, a RAP battle song, no personal insults, no family name dropping. Cole just didn’t have the heart for it and bowed out when, like you said, he should have just never said a damn word if he didn’t really want war.
I really don’t think Drake had/has any reason to be mad at Cole and withdraw friendship, if they were ever truly friends to begin with. Drake’s issues with Kendrick were personal in nature while Cole/Kendrick would have been nothing more than a contest for the number 1 headband. I could see Drake, as an MC, being disappointed that Cole withdrew but Cole don’t owe Drake a damn thing when it comes to how the battle played out. It would have been corny as fukk for them to “team up” against one rapper and made both of them look weak. Cole even directly acknowledged that Drake had done a lot for him throughout his career and he appreciated it. And he did it AFTER Kendrick threw down the gauntlet and said that anyone sympathetic to Drake was an opp in his eyes.
Basically the outcome of the battle doesn’t reflect on Cole, it reflects entirely on Drake, his actions, and how he handled himself. Just like Cole has to live with how his legacy will be perceived from here on out for not battling, Drake has to live with the dame thing but with choosing to engage.