I'm sorry. I know this is probably not what you want to hear, but your boyfriend is the one being rigid, controlling, and unreasonable. Mature adults understand that it takes time for children to get used to a parent's new partner, that it is threatening for the child and takes time, patience, and a long history of positive shared experiences before the child can become receptive to the idea of someone new in his parent's life.
It's up to the child's parent to put the child's needs first (not saying allowing the child to control---just putting his need for emotional security and stability and time with you first). It is up to the new partner to be mature, understanding, and patient with this process and allow the child to become acquainted over time.
Your boyfriend says he loves you and sees a future with you, but he MUST realize that any future with you INCLUDES your son, with your child's needs coming first. Maybe your boyfriend just can't wrap his head around this quite yet.
IF he is willing to work on expanding his concept of the relationship with you to include your son, it would be helpful to do so with a trained marriage and family therapist or psychologist specializing in this area. This means that you and your boyfriend would attend sessions together to help navigate how your relationship will need to grow to include your son. It may also include your child at a later time, if the first part of the therapy progresses well.
Right now, your boyfriend just wants it to be you and him. Well, that's not at all realistic. If he can't or won't commit to recognizing this relationship includes both you and your son and to working on being a positive, kind adult who will also share in your son's life, then you will have to ask yourself why you would ever settle for a such a man and why you'd subject your son to such treatment.
Again, not trying to be harsh, but it would be sad to waste your time and hurt your son in the process if this guy (who's also a parent!) can't see that your little boy's needs must come first here.