Hm, some psychologists aren't afraid to say "suicide" or "cutting." Saying "hurting yourself" covers a broad range of things so in some ways it's not really a euphemism if you say it bluntly. So that way if someone has been resisting the urge to hit themselves with things or burn themselves etc then "hurting yourself" applies to them too, but they'd be missed if you asked about suicide and cutting.

But the fact that they mumbled "both" isn't good -- they should be able to be straightforward about it. It's probably something they're just personally uncomfortable with. Self-harm can be frightening to people who don't understand it, and still uncomfortable to people who don't know what it's like to rage against your body in that way.

When I'm a psychologist, I'll probably ask "thoughts of hurting yourself" because it's broad -- but I won't be scared of self-harm talk. I look forward to being a very frank professional. It will be very hard to shock me.