Daddy simply can NOT take this personally. This isn't a personal thing at all. If fact, this sort of thing will happen off and on through out your lives; sometimes he'll prefer you and sometimes he'll prefer daddy AND there will be certain things he'll want to share with one more than the other. This is NORMAL.
You said this started when he began teething. Well, mommies are the comforters...especially if you're breastfeeding--and no you shouldn't stop due to this.
I promise, promise, promise this will pass.
As has been said before, you can start picking out responsibilities that belong to daddy...as a general rule this is good anyway.
Honestly though, I think this simply has to do with a situation, not an attitude or a like/dislike issue.
Watch for how you respond when he starts crying.
~~Are you compelled to come rescue him?
~~When daddy's holding him, do you allow time for daddy to sooth him in his way or do you put a time limit on how long you'll allow it to go?
~~Is baby actually reaching for you or are you offering yourself to him and he comes?
~~How are you holding him versus how your husband holds him? Sometimes it's the manner in which we're holding our babies that makes the difference. If they're in pain sometimes the WAY we hold them can HURT...so chech that out. Remember, too, the size of your arms compared to the size of daddy's come be the deciding factor, too. You may prefer to hold him on your left side while daddy's holding him on the right side; in general, babies prefer the left side of whoever's holding them because of they can hear the heart beat.
~~How do you talk to baby versus how daddy does? Are you softer and higher?
~~Do you stand, bounce, rock, etc...while holding your son? Does daddy?
This isn't going to last long, I'd encourage daddy to be active in the supporting role rather than getting hurt by this. I'd also encourage YOU not to get wound up in this idea that your 3 month old baby who is not capable of being mean is trying to be hurtful to daddy. Sooth hubby with specific language that aserts he's an amazing daddy rather than that he's missing out.
Be encouraged, this WILL pass. :o) :o) :o)