Why don't deer look up?
Well... they do... just not very often!
In general, I think it’s reasonably accurate to say that roe deer spend very little time looking up (apart from when they're feeding on relatively high tree branches, etc.).
The reason for this is because in an environment where the roe deer do have natural predators (i.e. on the continent, where their main enemies are wolves, lynx and bears), nearly all their threats tend to come from a ground-based assault.
In fact, this is true in Britain, too, except, although adult roe deer have virtually* no land-based predators, humans are by far the biggest threat to their lives. (Foxes do predate on young fawns.)
*I said virtually because it is entirely possible that golden eagles and white-tailed sea eagles do take a small number of adult roe deer every year.
However, as shown here, they do look up every now and then. Roe deer are incredibly adaptive animals and they have evolved to live in a habitat where they do face an occasional aerial based assault; attacks from golden eagles in the plains and forested areas of Russia and the far east.
So, in summary: Roe deer spend nearly all their time looking across the land, rather than up, because what where the vast majority of dangers to their life come from.
About the photo above
Technical details: shutter time 1/800 s, aperture f/5.6 ISO 10,000 focal length 800mm. Very cold conditions in December.
It had just started to rain at the time and the droplets landing on her head caused her to glance upwards. This image was taken during the process of her moving her head up, just moments after this photo was made, she extended her head to such an extent that she was looking almost vertically.