Do we have fundamental conflict in biology?
Peto's Paradox is a great one. This addresses the disconnect in cancer incidence with cell number in an organism. It goes something like this:

Assume current oncogenesis theory to be correct in that mutation acquisition is the rate limiting step in creating a cancer, such that you need ~5 specific mutations in a single cell for that cell to be fully transformed into a cancerous cell. This then being the case, it is so rare that any cell can acquire all necessary mutations that in humans we don't see cancer incidence appreciably increase until the 5th decade of life.

Now, let's assume man has an average weight of 50kg and a blue whale has an average weight of 130000kg, with roughly equivalent lifespans. Assuming average cell weights are the same in both organisms, there are 2500X more cells in a blue whale than a human.

If linear mutation rate is the rate limiting step in cancer then increasing cell numbers is akin to increasing the number of times you flip a coin to try and get heads, which means there is a 2500X greater chance of getting all ~5 necessary mutations in a single blue whale cell than in a single human cell. If human cancer incidence starts to spike at 50 years, this means blue whale cancer incidence should spike after 7 days and blue whales should largely be eliminated by cancers within the first month of life.

Hopefully makes you question a bit what is causing cancer.
Make sense?