It is due to the context of the sentence. If one has an intense career, likely, one will spend lots of time with work or out traveling, so one will NOT have time to be with family and friends. Hence, "away from" means "not being with".
If you choose "for", then it means "one will HAVE time to with friends and family". That contradicts with "intense career".
2012-12-05 23:24:48 補充：
by the way, you need to look at the phrase as "away from family and friends", not "spend away".
2012-12-06 08:03:02 補充：
one will HAVE time to with ... ==> one will HAVE time to be with ...
2012-12-06 12:01:31 補充：
The truth is it doesn't matter you choose "on", "with", or "for", they will ALL contradict with "intense career",