He's a boy and he's 3yrs old - his Dad is like Batman to him!
When my nephew was young we were really close. I looked after him alot, even from as young as 6weeks old (no issues my SIL was just very - I need a break for a couple of hours). I was young myself, just 19yrs old, but he couldn't have been in safer hands with me. I loved the bones off him.
Anyway, we were super close. Then I got a boyfriend and honestly my nephew just ditched me 😂he couldn't have cared less about me. My boyfriend was a tradesman and my nephew just thought this was epic (thanks bob the builder!). 2 yrs later and the relationship ended and we had to break it to my nephew who was devastated. He was just 5yrs old at this point and after he stopped crying he said to me - 'you don't want to be friends with Dave? Was he mean to you?' and I said, 'a bit, we fell out so I'm not his friend anymore, but he's still your friend'. To which my nephew said, 'Well, I'm not his friend anymore either then'.
Anyway, this is really just a convulated way of saying - your his Mum. He's likely going through a Daddy hero stage, he can give you all the bad side because your his Mum and when push comes to shove - your his Mum.
A younger sibling doesn't change that. It may just have intensified something that was possibly inevitably going to happen (a bit of Daddy worship) but I have alot of friends with first boy sons who have or who are going through similar and feeling a bit teary eyed rejected.
Think some of the replies are unhelpful, you need building up and remotivating - not taking down. Being rejected by your child is not easy, it might be perfectly normal but we're human, not made of stone. But there's loads of really good advice and empathy in the thread too. Focus on that.
I'm guessing you wrote this because you're hurting as much as you are frustrated. It's understandable to have a "this will never get better" moment (we all have them - I had one today after an epic toddler meltdown - I was feeling very sorry for myself) but I hope it's just that - a moment - after the end of a hard day.
Say to yourself - alright lad, you might not like me but I love you, so show me your worse, whatever you got, because I'm going to keep showing up for you'.
Repeat that a million times a day in your head, until you feel that strong and at some point, I promise he's gonna melt in your arms because all he wants is his Mum.
Remember at 3yrs old they're after independence and him seeing his Mum with a baby might be him associating you with 'babies go to Mum' - in 3yr old speak 'I'm not a baby, xyz is the baby, xyz cuddles with Mummy, not me because I'm not a baby'. If that makes sense?
Soften up a bit and don't resign yourself to anything. No matter what - he is still your baby.