suddenly when war comes is only mandatory for man
The german constitution restricts drafting to men[0] and would have to be changed before such a law could even be considered.
Before you ask, yes, the constitution also says that men and women need to be treated equally[1]
Just to add, the current government does not have the necessary majority to make such a change. Therefore making a law which includes drafting women is legally impossible without opposition collaboration.
Is there anything in the constitution that forbids the government from requiring citizens to perform some kind of service to the government?
dig trenches
carry heavy rucksacks
move weaponry and equipment by hand
survive hand-to-hand combat (granted, their odds are still limited to below 50%)
There is nothing about males that make them more suited to be doctors. We also can see that in the demographics in some countries (e.g. the UK), there is a roughly equal balance of female doctors to male doctors.
Having mathematical ability is linked to intelligence, not sex.