I think it's fine to be a bit selfish about reasons not to have another because it's essentially about the lifestyle he wants for your children and him and you as a whole. If your eldest is 6 and he's not allowed to do the sport until I guess this imaginary 3rd is 4, that's potentially another half decade or more of not doing the sport, and with already over half a decade off, there's a chance that he'll age out of being able to play it at a certain level and will have lost well over a decade of doing something that I'd guess brings him joy, community, a sense of achievement, passion, physical activity in a form he enjoys, some friendships, all sorts. If my husband wasn't allowed to play his sport while our children were young, he and we would've lost so much of what enriches our lives as a whole family now.
I'm not saying a sport takes priority over a child but I feel like it's totally fine to say I love these 2 children we already have, I'm happy with our family unit but that I also want and need to do something with my time that's important to me.
I'd have loved one more baby but financially it just didn't work out at the time and now my youngest's 14 and I'm so happy with the life that we have with the children that we did have. We had ours much younger than most of our peers and we're getting that freedom and independence back into our lives now. And I love that we can do more grown up things with our children now that they're all teens. And I think it's been good for them to see both me and my husband pursuing our hobbies and interests and passions outside of work through sports, music, volunteering etc. That sport that my husband continued to play is now a big passion of our boys, he coaches one of the teams, they spend so much positive time together because of this sport. Sure, it's tricky when they're very young but we'd go and watch him, or when they got to an age where they had their own weekend sports and activities, he did his thing and I did the kid thing and it was fine because I did my things on weekday evenings.
One more baby becomes an extra child, an extra teen, an extra adult, an extra meal at every dinner out, an extra seat on every travel plan, an extra room on holidays, a more expensive bigger car, a more expensive bigger house, and so on. Even without the private schooling, it's not just a baby, it's a whole life.
But I do get it. I had great births, I enjoyed parenting, I think I did a decent job of it. But I've had to reflect that it was enough to do that all well for the number of children that we could afford not the number of children we could physically have. My husband was from a very large family and he really wanted to make sure we could give our kids the kind of experiences that he wasn't able to have when he was young because there were always so many people.