In my opinion breastfeeding helps with bonding and the babies immune system. It's a good opportunity for mom to rest while doing so. Would he expect you to lay the baby in a crib and prop it's bottle with a blanket? Why exactly does breastfeeding bother him? Is he the babies father? (Oh, I see others asked you that already) I'm a bit disturbed by the question frankly. When my three sons were babies we couldn't be separated. My husband never complained because we were very close and it just wasn't an issue. But if he'd have said something similar to what your *man* said I'd have found it to be indicative of a serious issue and told him to back off. Your treatment of and closeness with the baby is foundational. If you choose to cater to this man's suggestion, what's next? The baby comes first because it's helpless. Others here have advised you properly as well. If you're in a loving relationship this shouldn't be an issue. If not, you need to think about his influence moving forward.
I wonder also, is this man the baby's father? It's a concern either way, but a new guy who doesn't want you breastfeeding your baby is a more serious concern, IMHO, and foretells other things he'll do to come between you and the baby. Either way, dad or not, it's immature and selfish.
Your baby is going to be 100% dependent on you for a while because he/she is totally helpless right now. Most normal adults understand this and accept it as part of being a parent. Your "man", whom it's not clear whether he is the child's father or not, needs to grow up and realize that your child is your priority and rightfully so. A real man who truly loved and respected you would never be jealous of a helpless baby. He sounds extremely immature and not really worthy of you. You really need to sit him down and have a conversation about this and determine what is his deal and whether he's capable of understanding the situation or if he's going to continue being jealous of a helpless baby.
Is this just one of many complaints that the baby is taking your attention from him? If so, you need to talk about the issue (of his feeling neglected), it's not the breastfeeding. If this is the only way he is feeling put out, he might be jealous of the breast being something for the baby. In either case, I'd consider couples counseling. If he is going to be this demanding at a time when you are busy and worn out, I can't imagine he is suddenly going to be more understanding of the needs of a toddler, middle schooler, or teenager. See a counselor and don't stop breastfeeding just for this reason -- it is great for your baby, their body, their immune system and their brain all benefit.
I'm sorry to read this. This is a difficult situation because a man jealous of his baby and feeling like a mom with an infant is too 'into the baby' and needs to stop breastfeeding kind of falls into the selfish category. I hate to say that and hope I'm wrong. It IS a jugging act to wear all your hats. Mom has to come number one in my opinion but at the same time, you should also pay attention to your marriage. I was blessed with a husband who understood I had only so much energy and our children got the better portion of it when they were little.
I saw a funny meme that said "what mom's really want is for their man to take them lovingly in their arms and put them in bed . . . and while they slept soundly, their man cleaned the whole house" Lol. But so true.
However, you are in a pickle because it doesn't sound like your partner is understanding. So, I'd plan a date night every week. This does not need to include a sitter--- you can put the baby to bed and do it at home after. Rent a movie, light candles, have a bottle of wine, snacks, music, conversation. But all your focus is on HIM. And DO once in a while get a sitter and go out as a couple.
I would not discontinue breast feeding unless YOU want to. And let HIM know that if you do, GREAT, cause then HE can get up and do some of the feeding of the baby. :>) His child work load will increase if you aren't breast feeding. But kids still require a ton of attention and if you aren't giving it through your breast, you are making a bottle . . . so, it's never going to end. The attention to kids. I WILL say that when I nursed, I had a lower sex drive. And it was nice to get my body back (sort of). But I was still all in as a mom complete with spit up on my shirt, hair needing combed and tired eyes. But if you are ready to wean your little one, then do so.
Giving attention to the relationship is important too, don't get me wrong. That's the foundation of your child's life---- that you and your partner are happy together. So, it's a balancing act. hugs