I have to agree with much of what has been said in the last couple posts here. Lincoln did not accept secession as legitimate, and therefore, he could not give into demands made by the CSA, such as offers to buy Federal property. Now, for the most part, they had just taken arsenals, naval yards, and the like when the states seceded. But there were two posts that they could not touch: Ft. Pickens and Ft. Sumter. These two forts were occupied by Federal troops and the only way that the Confederates could have taken them was to storm them, which would be an act of war. They, as we know, didn't want to be the aggressor, though thats how it ended up in the end. Therefore, their only recourse was to offer purchase.
What else could Lincoln do? He does not recognize the Confederate government as legitimate. He is doing his best to make the European nations see it that way too. But if he goes and sells the last two remaining Federal strongholds in the South (one of which never fell to Confederate hands) then he has given them legitimacy and said that secession is a right that the states do have, and that opens an even larger can of worms (because then New York City could secede, as they threatened to do, even though I don't think they would have anyway, and also possible New Jersey, which pondered the question a little as well.)
When Lincoln took the oath of office, he vowed to uphold the Constitution of the United States to the best of his ability. Now Article 1 section 8 does say that Congress has the power to hold authority of Federal installations, but they cannot do that without the president per se, because each branch can't operate separate of the others (even though the USSC seems to think so :laugh1:.) And the oath does not say that he is to uphold Article 3 of the Constitution, but the whole document. Lincoln was doing his job, and any president who did not do the same would be thought of as derelict in his duties.