I've read many times that lifting to complete muscle failure is extremely taxing to your body. Additionally, tendons & ligaments are slower than muscles to become accustomed to weight training - thus the number of injuries caused by lifting to failure.

As someone else posted - if you're lifting to complete failure, your form is probably compromised, which can lead to injury. You should lift until you cannot complete another rep with good form.

Pushups - my wrists are bad also. Instead of putting my hands flat on the floor, I grasp two dumbells to keep my wrists straighter. If your feet are slipping try a non-skid mat or wear sneakers. If you're getting dizzy, start with one or two. You'll be doing pushups like a Marine recruit in no time!

Also, if you're riding a bike and lifting 3X week, you might begin to exhaust your body which is to be avoided. Training is riding that delicate balance between pushing your body to become better, but not tipping into exhaustion.

I lift by myself, free weights and some machnes, in a gym. I don't worry about a spotter because I'm not lifting to failure - no where near it.

Lastly, if I just ride and don't lift, I become flabby. Even in the legs. It might have to do with slow twitch vs fast twitch muscles - some women on this board seem to have earned muscles on their bikes!