I think you might be:
My first half is usually sturdy
A DAM must be sturdy to hold back enormous volumes of water, form reservoirs and prevent flooding.
The second is mostly relative
People will commonly say that 'AGE is relative' - "you're only as old as you feel", and all that. (Plus the difference in two people's ages can show who's been alive longer - i.e. it allows a relative comparison to be drawn...)
If the first is not well maintained
I shall greet it with the second
If a dam is poorly maintained it will show signs of age and wear...
(Plus, as the OP prompts in comments, 'greeting' the first half, dam, with the second, age - i.e. putting them alongside each other - produces damage, the direct result of 'not maintaining' the first, i.e. a poorly maintained dam will result in damage, both to its structure and potentially to the valley and settlements below in the event of it bursting...)
Regarding the hints:
It does not often hurt the culprit to damage someone or something deliberately (through an insult or violence) but it is often physically and mentally scarring for the recipient. 'DAMAGE' is 6 letters long, and everything on our planet has an 'age' as everything has come into existence at some point.
As for the title:
If you are unfortunate enough to encounter something traumatic it may cause you damage - but you would never wish for it (it is unwelcome).