I've seen this criticism repeatedly. Maybe it has merit - after all she was raised vulcan, and her main story arc is her inability to successfully compromise between her logic based detached up bringing and the fact that she is a human with real emotions that can't be ignored. Thats her story, and its difficult to see how 'likeable' such a character can be.
Leaving this aside, where is it written that a lead has to be likeable? That hasn't been an expectation for years now. Nevermind the fact that there are a number of intentionally 'likeable' characters in the show to appease fans (Stamets and Tilly for example).
As I explained in the rest of the paragraph that was excised, it is her background as a mutineer that makes her unlikable, in my mind. Had she simply made a tactical mistake and the redemption arc was built around her learning to become more seasoned, I submit my reaction would've been very, very different. Instead, she substituted her seven years of experience in Starfleet for that of a seasoned, battle-hardened commander of decades of experience--her mentor and friend, mind--on a one-in-a-million chance that she was right in assessing the strategic background of the situation and Philippa was wrong. And, what's more, Michael was wrong in that assessment.
So, no, it isn't her, per se, that I find unlikable. It was her actions, her behaviour. Her redemption arc, for me, is a delta that goes up a steep cliff and one I will probably never fully accept (in part because of the arrogant presumption by the writers that mutiny is a redeemable action in anything other than extreme circumstances; a slap in the face to those who actually understand what a chain of command is and why it exists). There are very, very, very few circumstances where mutiny is an acceptable option. Not one of them are present in the pilot episodes. I think that was a storytelling error on behalf of the creators because, at least for some of us, that fatally compromises their chosen protagonist.
And that's the problem I see with your second paragraph. Protagonists are supposed to at least be relatable. I find nothing to relate with Burnham about. She was wrong strategically, she was wrong tactically; she was arrogant, presumptuous, and contemptuous of those who she should have been supporting. How am I supposed to sympathise with that?
As for the assumption that Stamets and Tilly are 'likable'...well, to each their own. I find neither particularly likable, though Stamets has grown on me a tad in a grumpy-but-not kind of way.