Homeschooling Support Group
This community is dedicated to parents, educators, and students involved with home schooling. Home schooling - also called home education or home school - is the education of children at home, typically by parents or guardians, rather than in a public or private school. If you have chosen to provide education to your children at home, join the group and get support.

This is a perfectly appropriate place to ask the question you posed. Though, for some reason this page hasn't been very active recently.
I don't have a child who is gifted or advanced, rather I have a child with multiple challenges all or most of which are unrelated to any challenge I ever had. And, I feel that the school has failed us in areas of education and safety.
13 can be a difficult age (my son is 14 now). He's probably right on the cusp of realizing that no one knows everything and that he is sometimes in life going to need to respond respectfully to someone who lacks his knowledge but exceeds his authority (in this case the teachers, later bosses, shareholders, ceos etc). Or, to someone who needs his information but "just isn't getting it".
If his new school doesn't work you still have a couple of options. Homeschooling is great for some and may work for you. You might want to consider first the time investment required and whether his areas on interest match your areas of expertise. You would want to facilitate the situation in such a way as to avoid being the target of his contemptuous behavior. You could get as advanced a curriculum as he needed and some college classes are also available fully online.
If he's reading on a college level and far advanced academically, could he handle both the academic and social/philosophical complexities of taking a class or two at a community college (in some places called junior or city colleges). The social philosophical aspects I'm referring to are that a lot of typical students there are in their early to mid 20s, smoke drink, and are in open rebellion against all things parental - not all of them, but a lot. So, the idea comes with possible benefits and some potentially huge detriments.
Another option:.To challenge him could he pick one of his pet subjects and develop (with help, as needed) a class to teach at local libraries or afterschool programs to younger kids to help get them interested in the subject. Does he have the patience and tact /diplomacy for this yet? (I never would have thought of this, but I saw another parent use this with one of their kids).
These are surely not your only options, but are all that come to mind right now.
Sincere best wishes. I hope you find the option that works best for you and your son.
Beryl
Anyway, if you homeschool you have the freedom to let him use a language arts/reading/literature at the grade level he really is intellectually (not by grade by age). I actually posted a video (VLOG) at my YouTube Channel about some really GOOD literature rich curriculum. If you want to check it out, please do: https://www.youtube.com/watch?v=DAOTg89doA4
Also, Homeschool Curriculum is catered for all learning styles. You can do your research and find ones that best fits with your son. It's not an easy road, but well worth it! My biggest advice is to pray first and give it a couple days, research your options, pray some more:) ~and then make your decision from there. ((also, are you married? if so, it's also important that you and husband are on the same team about homeschooling.)) ((Also, google "homeschool conventions" for your state and try to attend one- that will probably give you the biggest eye opener into what homeschooling is all about)) ~~Good Luck, God Bless!