Given that the Lincoln administration wanted to close off the seceding states from exterior resources and assistance, there were two known methods of doing so:
1) Port closure. The simpler and less-expensive of the options; the country simply declares one or more ports to be closed to entry. This is administered under municipal/domestic law and litigated in the usual court system of the country. It does not require military presence to be enforceable, but to be practicable it requires a civil/enforcement presence in the ports in question.
2) Blockade. The more elaborate and expensive of the options. Under certain conditions accepted in international law and diplomacy, a country stations warships off the coast of another country to prevent ingress and egress. This is a creature of international law and the law of war and is by definition a military action; related legal challenges are mounted in special-purpose courts ("prize courts") and among the diplomatic representatives of the countries affected.
Because blockade presupposes an armed conflict, and a war presupposes an enemy, the way the treaties were written presumed another country, generally called a "belligerent" or similar term. Under the mid-19th century understanding of international law and the law of war, belligerency conferred a certain set of accepted rights and standards upon the belligerent, as well as a sort of de facto legitimacy. This conferred legitimacy was what Lincoln's cabinet would have vastly preferred to avoid, because it was logically inconsistent with the stance that the seceding states had not left the Union to form a separate country. Significantly, Navy Secretary Gideon Welles argued strongly for port closure and against blockade, based on this very conviction that the 'states in revolt' were not a separate country and therefore international law was inapplicable. (It also would have been considerably easier on the Navy to not have to mount a massive blockade of a 3,500-mile coastline.) (Much of what's said in many places about the closure/blockade debate is derived from Welles' recollections, and is filtered through his opinions.)
The Catch-22 here is that, since port closure is domestic and does not apply internationally, it doesn't apply to any other nations. In order to conform to a port closure, those other nations would have to voluntarily comply. In Britain and France's case, they saw this as a naked attempt to enlist their assistance against the rebellion, and therefore a violation of their own declared neutrality. (Seward tried to do this as well with offering to sign the 1856 Treaty of Paris outlawing privateering, which would have required France and Britain to help catch Confederate privateers. They didn't want to get involved at all in that, either.)
Blockade was the sole acceptable option from Britain's and France's standpoints. There was an established body of law to define and support it and well-understood customs and procedures. This was not a decision the U.S. could make unilaterally without significantly harming its relations with the other powers; as such, Seward was a strong proponent of blockade as opposed to port closure (and came in for a good deal of pen-lashing in Welles' writings as a result).
Essentially, it was the pragmatic reality of the situation that swung the decision toward blockade from port closure. The Lincoln administration had to face up to the fact that to maintain ideological purity in the stance of 'no separate country' that they would incur the wrath and opposition of other nations, and thereby make that 'separate country' all the more likely to exist.
It was not a decision taken lightly at all, nor an uninformed one. Even still, Lincoln tried to have it both ways by the wording of his blockade proclamation, justifying it in terms of collection of customs duties, but that was ignored by Britain and France.