Of course it’s not a sin.
What sort of education one chooses to enroll their child in is ultimately a matter of parental discretion and involves weighing all kinds of factors.
I, personally, believe that public-funded education is a good thing. I acknowledge that, depending on where one lives, the quality of that education can vary wildly. If parents are able to afford quality private education for their children, that is also a wonderful thing. And if parents have the luxury of time, resources, and are themselves qualified, then homeschool can also be good.
There is no right or wrong answer; the right answer depends on dozens of factors; and ultimately is a matter of things like conscience, wisdom, and practicality.
If I offered my own personal experience growing up. I received a private education at a church-affiliated school from K to 6th grade (I’m using American terminology, for those who use other terminology based on their own country’s system and metrics); some of it was just fine. However on the whole the school was low quality, and it set me back, especially when it came to mathematics; it was also an awful experience as my family did not belong to the church it was affiliated with, and children of non-member families often faced challenges other students didn’t. Teachers routinely targeted such children, myself included, for social ridicule so that we knew we we did not belong. So my private school experience was quite terrible.
I was also homeschooled for a year in my junior high years, both my parents worked and so they used a mail-in VHS service from Abeka through Pensacola Bible Institute. These were VHS tapes recorded from real classroom settings. These came with coursework which had to be completed and mailed back to Florida. These VHS classes were absolutely terrible. They were, of course, what one would expect of a low quality VHS recording from the early 90’s, but they were also entirely unedited. As such if a child acted up in the classroom, the teacher would break from the lesson to scold the student–sometimes interrupting the class for as much as 5-10 minutes at a time. Sure, that may have been a true-to-life classroom experience in a way, but I already hated having to sit at home by myself in front of a TV learning a subject from the most boring teachers I could imagine (while avoiding the temptation to just turn it off and watch cartoons or something instead); but then have to endure these interruptions as well.
Awful. Simply awful.
As such, when I attended public school from 9th-12th grade, it ended up being, in fact, the best education experience I had at that point. The quality of the education was certainly the best I had had up that point. I also, for the first time in my life, developed the ability to socialize with people my own age and make friends. Up until public school, I did not really have any friends. As such the majority of my childhood was spent by myself. I had to, effectively, learn over a decade of social skills in a very short period of time.
Public school came with its own challenges. But on the whole, even counting the bad experiences, it was still the best education experience of my pre-adult life.
Now, none of this means I am opposed to homeschooling or private education. I think both are perfectly valid educational options for parents who are capable of it. I am saying, though, that my personal experience means I do have a particular perspective: I can’t, therefore, simply say that homeschooling is always better than public schooling. Because that certainly isn’t the case.
So I return to my position made earlier: This comes down to weighing a lot of factors and making an informed decision on what one believes is best for their children. And not all parents will reach the same conclusion; nor will all parents have the same options available to them. Not all parents have the means or ability to do certain things. For some parents, public education is the only option, even if they may believe homeschooling or private schooling would be better. The circumstances of life differ for all.
So at the end, parents simply must do what they are able to do, according to their means and conscience.