I would be happy for someone to prove it wrong. Is there any basis in Scripture for the prohibition against meat, or is it a “church” thing?
There is no “prohibition against meat”. Such a prohibition would imply that eating meat is somehow evil, a strange notion that is completely inconsistent with Scripture.
The periodic abstinence from meat is a mild form of fasting, a practice recommended throughout at least the New Testament. The disciples are mentioned as fasting in Acts 13 & 14, in Matthew 6 Jesus tells us how (not) to behave when fasting, in Mark 9 Jesus informs us that some problems can only be dealt with through prayer and fasting.
So there ... you see that it is a Scriptural thing. This should make you happy.