When your attorney pontificates, saying "The law favors the assignability of contracts," he or she just means your deals can be bought or sold, or, in legal jargon, "assigned." Thus, you could shake hands on a deal with one person and end up doing business with another. Like all things legal, the general rule has many exceptions. For example, the term "assignment" really means two things: the sale to a third party of one side's right to receive something from the other and/or the delegation to a third party of one side's duty to do something for the other.
If you don't want the other side to be able to sell your deal, say so in your contract: "Any assignment of this agreement by [the other side] is void." Conversely, if you want the unrestricted right to sell the deal, spell that out. Or consider a compromise: List which assignments are OK and whether they require any notification or approval.