I never got why putting up one of your own is such a popular strategy.

A lot of times the alliances are fairly evenly split. If you put up one of your own that is one less vote your side has. Makes it so much easier for the other side to find the crack and get someone who isn't happy in the group to flip.

In this case it it seems it is

Renny
Keesha
Dan
Memphis

vs

Ollie
April
Jerry

The three are not going to save anyone in the four if they get HOH next time, so why placate them. Although I'd put the pair up so the one can't save the other.

If you put 2 of the 3 up they only have one vote left out in the house so the votes would likely be 4-1 or 5-0 as they may just go along with the house vote. Or if everyone just splits the votes up at least one of the people going home isn't on your side.

If you put up one of your own you are now at 3 votes to 2 and all the three have to do is flip one person rather than having to flip several people.

I don't see why taking away a vote that you may need to keep the balance of power is considered a safe thing to do. Now I do understand the you don't want to be the one in your group that goes up next, but you want to have your group be stronger rather than weaker after your reign. You screw over your alliance and make them weaker in the house they aren't that likely to come to your rescue when you get put up.