Thanks to @MTFU_Training for the quote. cyclefucius gets it. And has sometimes been guilty of replacing rides with weights due to unappetising weather, lack of time, excess of lethargy etc.
But what about:
1. core strength: cyclefucius posted recently about this. It helps with and is hard to get just from bike riding. Triceps may also fall into this category.
2. you will fall off: cyclefucius say: you can fall off with no body strength or fall off with body strength. You decide which is better.
3. bones: mountain bikers are a bit better off than roadies but like a hungry baby long times in the saddle suck the goodness out of your bones. Not much point having your well trained heart, lungs, circulation etc. outlive your bones. There’s a lot of dodgy science out there but this seems hard to deny. See also no.2.
4. balancing out your body: cycling exercises some bits but not others – do the math. Unless you are a pro-rider with 4% body fat, a huge bottom half and a pasty scrawny top half is not what we are going for. (cyclefucius seems to remember David Bowie saying that he put his body all out of balance at one stage by doing only bench presses and situps – anyone else remember this interview?)
5. vanity: if you are reading this then there is no way this will apply to you.
The real answer? Today I am MTFU and doing both.