I used to say that by the time my kids were 10 they'd have the majority of the say in this choice. Then my eldest wanted to check out school (out of curiosity, and a concern that she was missing something crucial and meaningful) at 9, and I let her "shadow" for a week, after which she decided "meh." Now I have an exceptionally mature 8-year-old (my fourth child) who I think I would allow to attend school if she really wanted ... but she is fully capable of considering all sides of the issue and has understood that the limited social benefits would come at some pretty signficant costs for her.
So would I let a 7-year-old choose for himself? I don't know. It would depend on the 7-year-old, and the school.
I would certainly take the request seriously. Meaning that I would open, and continue, a dialogue to solve whatever the issues are. For instance, if he is craving social interaction, I would bite the bullet and join a support group or co-op even if didn't match up with my religious beliefs or homeschooling style. Or if there are no extra-curriculars you can afford to get to, I would *start* something if possible... a Roots&Shoots group, or a Reader's Circle, or a Family Bicycle Club, or a Children's Community Garden, or whatever, volunteering my time in an organizational or leadership capacity, possibly trading off younger-brother child care with a mom who has an older child who wants to be part of the activity you're running. I would take a more active role in setting up a roster of play-dates. I would get out and about more with him, even if it's just to a café for a hot chocolate, to the park, for a litter-picking walk. I would do whatever was in my power to fix the "mornings don't work" issue so that you can get to the secular homeschool group -- minimize artificial lighting in the evenings, move dinner time an hour earlier, institute a family tradition of a walk or a quiet swing and readaloud story in the hammock at 8:30 pm. I mean, really... if school is the alternative, that's going to involve early mornings in a huge way, so finding a way to manage mornings to serve unschooling is probably small potatoes compared with the that.
If it's the lack of structure and intentionality to his days that's bothering him, if he's so unaware of his learning because it's such an integral part of his life, find ways to draw his attention to what he's learning. And maybe consider ways to reassure him about the skills and concepts he's picking up. Find a general 2nd grade skills dollar-store workbook and let him at it: let him see that he can do much of what is technically a year ahead of his age-grade. Sit down with him and ask him what he would like to learn and how he would like to learn it: and if that entails structure and school-like materials, support him in that. Maybe that will get it out of his system, or else maybe you'll both discover that he thrives on it.
If he's getting disparaging comments about his education from his buddy, then I don't think occasional counter-indoctrination would be amiss either. If you get into a casual conversation that meanders into plate tectonics or the caramelization of sugar, or what "average" means from a mathematical standpoint, do a little double-take and exclaim "Oh! Isn't it lucky you're homeschooled! I didn't get to learn about this stuff until I was in high school [fifth grade, eighth grade ... ]!" Or if you're eating waffles at 10 a.m. on a blustery day, relish the moment by saying "This is so cozy and nice and relaxed. Imagine if you were Dylan, you'd have had to be out of bed three hours ago and waiting outside in that horrible weather for the bus!"
Rather than just seeing it as a "School? Or no school?" issue, treat it as a signal that something, or several things, need to change. Set about identifying those things, and make it clear to your ds that you see his dissatisfaction with homeschooling as an issue to be creatively and energetically explored and solved.