The biggest reason that I've started strength training is that it makes me feel powerful. There's just something about being able to say I picked up X pounds that makes me feel like I've accomplished something. It's tangible and I'm becoming able to lift greater weight with certainty. This is a huge contrast to my day job where one thing morphs into the next with no concrete end points. Having an actual accomplishment is great for my brain, it's like a checkbox on a list (LOVE lists for their checkboxes).
Lifting also gives me something to look forward to that's not work. I was reading an article on how to avoid burnout and it suggested and one of the suggestions was to stop focusing your entire life on work and get some hobbies. I'm finding that lifting as a hobby is great - it doesn't take tons of time (we're slowly growing our exercize room) and there's definite start and stop. I can do it alone for a few minutes a day, it takes all my concentration so my brain must stop mulling work-related items, and then I can move on in a more energized way to doing everything else around the house I want/need to get done. Plus, endorphins are AWESOME.
It's funny, but I've started sleeping better as a result of this exercize regimen. I wake up fewer times during the night and wake earlier feeling more rested. All this crazy regimen is worth it for that alone. I'm no longer the one who sits in bed trying to unwind while listening to my husband snore like a freight train (he falls asleep within a minute of laying down most nights). I hit the pillow and I'm out like a light. I don't feel like I need to sleep more on the weekend to catch up because I'm finally back to sleeping well during the week.
I'm feeling really lucky right now - each one of these reasons alone would make me want to take up this hobby. All of them together are icing on the cake.