mitigate or militate?
In among all those Latin words that came into English via Norman French was the verb militer, in essence to wage war against but also to constitute a factor either for or against something. The original Latin verb militare meant to serve as a soldier (a miles). So if something is militating for a particular outcome, then it is helping to make it happen. Conversely, if it is militating against the outcome, then it is working to bring it to nothing. You can militate for victory or defeat. Think of it as bringing in the troops.
Now to the word mitigate, another borrowing from Latin via French. This one ultimately comes from the Latin mitis mild, gentle, giving the verb mitigare meaning to soften or moderate or alleviate. Here you have an intensely bad situation which can be made better or mitigated. Legalising ice will, it is argued, mitigate the ill effects of having a black market.
Mitigate. Militate. The two words are close and not commonly used so it is perhaps understandable that when we reach for them we sometimes pick up the wrong one.