score:20
It's probably because Ganson--one of the handful of Democrats who voted for the 13th Amendment--was on the fence about this Amendment himself. Voting not to reconsider the bill is similar to voting "present" in order to duck a difficult issue.
First, Ganson voted against the 13th Amendment the first time the House considered it. He was widely expected to vote against it the second time too:
When the name of John Ganson, a New York Copperhead, gave back an echo of "Aye," much to the surprise of all, there was a burst of applause... (source)
It's well know that Lincoln and Seward handed out rewards to lame-duck Democrats who considered switching their vote to "Aye," so perhaps Ganson (himself a lame duck) was holding out for a sweeter pot. Perhaps Ganson was internally conflicted over whether the Amendment would help end or prolong the war. Maybe he would rather abolition didn't come up for a vote at that moment, but didn't want to be caught on the wrong side of history. Perhaps he wanted the 13th Amendment to pass, but hoped it would do so without his vote against his party leadership. It's hard to say precisely, because apparently historians aren't too interested in John Ganson in particular.
What is known is that the vote on the 13th Amendment was so tight that neither side knew if it had enough support when it came up for consideration in January 1865. Democrats like Ganson, being the critical votes, would have been lobbied intensely by both sides up until the moment they cast their vote, so it isn't surprising that Ganson's voting record demonstrates some vacillation.
Upvote:2
In an article in McClure's in 1898, Charles Dana writes that in 1864, when he was an Assistant Secretary of War, he had with President Lincoln a week before the Nevada bill vote, in which Lincoln was anxious about the 1864 passage of the Nevada enabling act because one more yea vote might carry the Amendment vote in the House. What Dana wrote was "Here [said Lincoln] is the alternative: that we carry this [Nevada statehood] vote, or be compelled to raise another million, and I don't know how many more men, and fight no one knows how long. It is a question of three votes [in the House] or new armies." Dana knew the men in question, and got the three votes (Dana notes that two were from N.Y. and one from N.J.) with promises of patronage appointments after the session's end, which--after the assassination--President Johnson did not honor. A study of the seven Democrats from New York who voted for the amendment make it reasonable to believe the two Dana then spoke with were Anson Herrick and John Ganson.
Upvote:10
Quite possibly for procedural reasons. There are a lot of little nits about parliamentary procedures that encourage weird things like this. For instance, under the older Roberts Rules of Order extant at the time, a motion to reconsider could only be made by someone who voted on the prevailing side in the previous vote. So if there's a chance the vote might fail, it pays to have at least one supporter actually vote against it so that they can put forward the motion to reconsider.
I understand that usually it is the Speaker (or in the senate the Majority Leader) who casts this vote against, but if he wasn't there at the time (as your note implies), it makes sense that some other supporter would step up and do it.
After looking over @twosheds' answer, I think he probably has the right of it. But I still think there's an important general point in here: That votes on parliamentary procedural motions like motions to reconsider, motions to stop debate, motions to amend, etc., are not and should not be seen as equivalent to a vote on the entire measure. I know it has become fashionable these days to rag on representatives who "vote for it before they vote against it", but things like this are part of the process, and it doesn't work nearly as well without them.