My Dad is 85 yrs old with Alzheimer's. I can ask him to take a shower & he replies "I already took one, " or he goes in the bathroom turns on the shower, doesn't get in, changes his clothes & comes out. I've gone as far as saying "phew, Dad you really are strong today!" Last night I sat him down & told him I was disappointed, and he asked why & I ask him why don't you like to shower? Explain to me, I was calm & just like we're having a good ole conversation. So he never answered me, but just stormed off to the shower mumbling. But he did shower! So when he came out I offered him a back rub, as a reward. It's so hard seeing my Dad this way.
Make sure there is a shower mat in the tub/shower to help Dad feel safer. With today's liquid soaps with moisturizers, and hair conditioners, it can make the tub feel like an ice skating rink. The tub mat I have is a bumpy one, not flat like the older Rubbermaid products. It gives me a better sense of not sliding.
Then there comes claustrophobia as we get older. I have that issue when in the shower now, thus can't wait to bolt. I do plan to remove the glass shower doors and go back to using a shower curtain. The doors make me feel too enclosed. If it wasn't for having neighbors, I would rather hook up the water sprinkler and run back and forth thru it :P
And inbetween showers, one can use baby wipes. They actually work !!