Why do grad programs ask for date of birth?
For a grad program, age matters a little bit because of little space there is in many programs. This is true of some high profile majors like medicine though not particularly true to others like Law. Public universities are tasked with graduating people who will contribute to society given that their education is A) subsidized and B) very limited in space. 

This is going to sound mean, but a 60 year attempting to enter med school is not going to be a good candidate because by the time they finish med school and residency, they are unlikely to work more than 10-15 years before health complications and/or death. But if you take a 25 year old, they will likely use that degree for about 40 years. Mind you, this is not true of all universities and certainly, private ones are not held to these unwritten rules so ymmv.