Your son took the lead, made his own choice, asked not to play -- and his dad is clearly so in love with sports that he totally ignored his child's preference. Your husband may say "Oh, I'm just letting him try different sports so he can find one he's really good at," but do you really buy that? I can't, after what he said.
We are not talking here about a kid saying "I don't want to do my homework" or "I won't do my chores." We're talking about a child asking to opt out of an OPTIONAL activity when he already has three other optional activities. He's not asking to sit home and stare at a computer game or turn into a couch potato.
I don't know where to send you from here, but if your husband is talking to your son this way when your son is only seven, try to imagine the relationship the two of them will have by the time your son is 12 or 14. Your son will feel intensely pressured to do sports he may not want to do, in order to have dad's approval and love. Your husband is showing your son this: Dad loves you if you play sports, period. You are a good kid if you play sports and stick with them No Matter How YOU Feel. Your son will grow up feeling that dad's love must be bought with sports.
And what happens when your son is older and it turns out other kids are better at some sports than he is? When he's not a star player, not the quarterback, not the best baseball player or the high-scoring soccer player? The pressure will get much worse. If your son's a star, wonderful, but what are the chances he'll be a star, realistically? What will your husband do and say then? What comments do you think your husband will have the first time your son says "I want to be in the class play this fall instead of playing ball" or "I want to spend the summer at computer camp or art camp instead of baseball camp/football camp/soccer camp"? That is -- if your son develops the courage to say those things. He might not, if his dad pressures him this hard. Then you'd have a frustrated child who does not get any say in his own activities.
Picture, too, how you will be in the middle when schoolwork gets more intense. At seven your son has relatively little homework. Picture older elementary school or middle school, when there is MUCH more homework, projects, etc. Your son will be so stressed that both school and sports will suffer badly and the results of academic issues in middle and high school can affect his prospects the rest of his life.
I think your husband needs a huge wake-up call now, not in a few years when your son is stressed out and rebels, or stressed out and doesn't rebel and ends up believing dad hates him for not being a star player.
Your husband sounds like the kind of man who needs to hear this from a coach, a school principal (preferably male) or another man who is involved in sports. I would enlist a male family friend to talk to him seriously about how over-scheduled your son is, and how much pressure dad is putting on his son. I wish I could say he could accept a talk about this from a woman principal or from you but -- I would wager he is not going to listen to anyone but an adult male who is into sports himself.
If your SON did the choosing, would he choose every one of these sports? You will never know if he might have been good at other things -- academics, arts, music, anything. He will never find out what other talents he might have. Sports are great but not at the expense of absolutely everything else.