The troops are instruments of government policy. I was/am against that policy, for various oft repeated reasons. I could go into them, but that would cloud the issue.
Define support. Wishing they don't come to harm? Hoping they don't get maimed, executed, tortured, burnt to death? Hoping they all come home?
That's my definition and in that case, how can I not support my own countrymen?
Furthermore, are you saying that there will never be a war you won't support, never be a government policy that you won't object to? If that isn't the case, then there will be a time you won't be supporting the troops yourself, going by your logic.