My main reason: actively and repeatedly using TOR when you're a relatively high-profile military person will likely raise eyebrows, maybe even focused effort to figure out why. There are many ways to get information out of computers - taking over their account and checking their activity is probably one of the harder ones.

Other than that, you have to be very careful to use it correctly without revealing who you are, and all TOR would do in this case is (essentially) randomize your IP address. If e.g. you're consistent with using TOR for gmail and there's a time that doesn't correspond to your TOR activity, it's basically a guarantee that someone else accesses the account, though you haven't found out who.

There are some problems with TOR (Some have solution):

1. Someone with enough resources can create and add to the network enough servers, especially entrance and exit nodes, to effectively nullify the TOR router.

2. Some web tools can have side channel attacks that break out of TOR and use the internet to get a specific resource.

3. Another popular side channel attack is fingerprinting the browser, best demonstrated by the EFF here: https://panopticlick.eff.org/

4. TOR itself might have a bug or a backdoor, although this is getting a bit into the realm of conspiracy.

This is of the top of my head, but I'm sure I missed some.

People who control the exit nodes could potentially see all your traffic.

Large intelligence agencies may have lots of honeypot tor nodes, you might get one of them