Currently DNA analysis is quite crude, basically enough to determine some genetic predisposition to illness and family relationships.
But there is indication that researcher might be able to find generic markers with predispose people to various conditions and traits (such as being left handed, homosexual, overweight, balding violent, psychopathic, etc.). Do you really want this information to be in the hands of big government and multi-national corporations?
Even if someone is genetically predisposed to some trait, there are additional environment factors which can prevent this from surfacing.
Why should a person who may have genetic markers to make them predisposed to violence, but was raised in a loving environment and taught at a young age to use anger management techniques and never hurt a fly, be discriminated against like someone who has countless violent acts against innocent people?
DNA should only be allowed to be freely collected, when people have the technology and option to change their own genetics, so that they are not victimized by discrimination.