Your kid is 7 years old. And he's just a beginner, approaching intermediate level. Of course he's not going to be good at stuff. Whether it's sparring, forms, breaking, recalling terminology, leading the class, etc. It's to be expected. This is absolutely nothing to worry about. Trust me, he will improve.
Your main concern is about him wanting to quit Taekwondo, since he's losing at sparring a lot. Have you asked him if that was something he wanted to do? If your kid doesn't like Taekwondo, for any reason, it's best to let him quit. You tell your son, "If you ever decide you're not having a good time and want to quit Taekwondo, just tell me. I won't be upset."
Here's what you may not be aware of, though. What you see when you see your kid sparring is him losing or doing the wrong thing, a lot. You see him getting visibly frustrated and upset. That's what you take notice of. But what you're not seeing is that he's doing things right every now and then. And during those rare times, he's probably secretly jumping up and down inside his head having a blast. You won't necessarily see that.
So what you should try to do is to look for him doing the right thing, not for him doing the wrong thing. Take notice of those times and praise him for it. Keep track of it in your head, too. You might start seeing that he's been making progress.
He's learning what works and what doesn't. Eventually, he's going to get better. At first, there's this big learning curve. He's been told a bunch of things, and they're all going around and around in his head. Of course he's going to be slow reacting to stuff. He's going down lists of things in his head and asking himself, "What did my instructor say to do in this case? Oh yeah, I have to..." And then blam! He gets hit. That's normal and to be expected. The next time he's in that situation, he'll remember what to do slightly faster, and eventually he's going to reach a point where it requires no thought at all. He just reacts.
And this is a young boy. At 7 years old, kids are not very well physically coordinated. Their nervous system is still working things out. Even if they decide what to do, they can't quite get their arms and legs to do what they want. There is an awful lot of things taking place that you just can't see from the outside. On the inside, there is nothing but improvement going on. But that's invisible to you.
His instructors have undoubtedly been watching him closely, also. They see what he's been doing. They know where he's at and whether or not he's been attempting the things they've been teaching him. They don't usually put a lot of pressure on kids to do stuff, though. They don't take the kids aside and tell them they're not doing the right thing. That would be a terrible thing to do to a kid. No kid wants that. Instead, they let the kids figure it out on their own in their own time. But they'll keep on showing them stuff, and eventually they're going to use some of it, and eventually something will work. When that happens, instructors really notice it. It's what they live for!
So one thing you can do is go to the instructor and ask if he's been watching your kid and what he honestly thinks about his progress in sparring. It's a good idea to just open up and tell the instructor that you're worried that your son might want to quit because of his sparring troubles. But also tell him that this is coming from you, not necessarily your son. It might surprise you what the instructor says. He might tell you that your kid has made a lot of progress and is right where he should be.
If the instructor says your son isn't getting it, you can ask him if there's any way of improving things. He might suggest private lessons, for example. Think of it like tutoring. Or he might ask for your son to come to more classes per week. Or he might partner your son up with another kid in class who's good at sparring and would be willing to take your son under his wing and show him stuff. Who knows.
But remember: You're the parent! Don't just do what the instructor thinks is best. Do what's best for your son. And try not to put any pressure on him. He wants to make you happy. Tell him you're happy with him no matter what he does. It's all about what he wants, not what you want, and not what his instructor wants.
Oh, one other thing. You said your kid's Taekwondo class has a large emphasis on sparring instead of forms, and maybe your kid would like the opposite. Ask him if that is really what he wants. If so, you might be able to find another Taekwondo or Karate school nearby that does put the emphasis on the forms or at least makes it more even. You can take your son to see a class and ask if he'd rather be there. There are many Taekwondo and Karate schools out there. Parents are usually attracted to schools that have big classes with many kids in them, but smaller schools are often better and more tailored to the individual. It's something to consider.
Hope that helps!