Harris was appointed to carry out the government's or war cabinet's policy of area strategic bombing which he carried out with dogged determination, not only because he was ordered to do so but also because he wholeheartedly agreed with the policy.
However, in early 1944 when Bomber Command was needed to switch to tactical bombing in support of the forthcoming invasion, Harris disagreed with the policy so basically ignored it, still convinced that area bombing was all that was required.
IIRC, as mentioned in another thread recently, it took a direct order before Harris would start allocating resources to tactical bombing.
Dresden in particular certainly wasn't Churchill's finest hour, especially as Harris was specifically ordered to carry out the raid. I'm sure I've read somewhere that the raid was at the instigation of the Americans.