Adding another two cents here.
Picture this scenario:
As per Ray Franz, the GB needs 2/3 of votes to decide on important matters, such as change in doctrines or policy. Now, when they were 7, a change could only be obtained with a minimum of 5 votes in favor. Conversely, 3 votes would be enough to block a change.
For the sake of argument, let's say that the majority of GB members wants to change certain important policy or doctrine. Tony opposes it, along with two other GB members, and by 4-3 votes, they manage to block the change. The situation deadlocks and drags on for months or years. The majority of others grows frustrated. To force a change, the only way is to increase the voting pool or hope one of the 'opposing trio' dies. Enter Kenneth Cook. Now the GB is 8. Again, even if this scenario (5-3), the 3 votes block the change.
Now, at this moment, it is decided that the GB needs more members (old age of some members, share the burden, etc). Enter Jeffrey Winder and Gage Fleegle. They were handpicked knowing in advance they'd side with the majority. Now, the scale has tipped. With ten members, a 7-3 vote means the opposing trio can be defeated. Imagine, knowing he's outnumbered, Tony threatening: "if this is approved, I will resign". There's a show of power, a vote is called on the matter, Tony is defeated, a change is decided. The other two see it as Jehovah guiding things and accept the will of the majority; but Tony takes no BS and sees it as mere politics, and makes good on his threat and resigns from the GB. He then must be seen as resisting the "holy spirit", spiritually weak, obstinate, proud, and therefore loses his privileges and reproached, though not disfellowshipped, and not asked to leave Bethel either.
So, why bring in two new members, when 6-3 vote (9 total votes) would suffice? Because they were already accounting for the possibility that Tony would resign, thus reducing the members to 9, and so, they wanted to keep their majority intact, also in the likely scenario that one of them might pass away sometime soon.