I've read in some articles that there are no military divers specialized in cave diving. Experienced private cave divers are of more help here.

Well, a so called former Thai Navy SEAL died during this rescue operation, so I guess they are.

https://www.theguardian.com/world/2018/jul/06/former-thai-na...

I'm sure special forces are incredibly tough and very skilled - I was just wondering whether there would be any reason for them to train in the skills relevant to cave diving.

Wreck salvage. It's not quite the same skillset as cave diving, but wrecks have many very similar hazards.

Of course, the most dangerous person is someone who thinks they know what they are doing.

There was a news story in 2004 or so, where a team of british soldiers got stranded in a cave in Mexico. To assist with local efforts, two brits flew out - one of whom, civilian firefighter Richard Stanton, was also one of the two brits who found the kids in Thailand.

While there may have been other reasons not to send a military presence to assist (I recall it being a rather messy situation as it was), it seems clear we know exactly where the expertise is here, and don't let silly 'special forces' bravado get in the way of getting the job done.