Argentina started a war with Great Britain in 1982 when their economy was suffering.
The Falklands, yes. Islands close to Argentina and far from Britain. Didn’t take very long for Argentina to lose. Turkey could send ships, which would be sunk by Israeli subs. They could send troops, who wouldn’t make it past Beirut. The guy may be crazy enough to try some crap - he did send ships to try to break a Gaza blockade years ago. He tucked tail and went home. I think this is mostly talk but you never know. If he wants to help, send food and medicine to Egypt.
Not to mention domestic security issues. If he takes serious losses at a war that is not in Turkish national interest he risks political stability and a potential internal coup.