I like Natasha, God knows she's been under attack in there, so we've seen her being defensive at times. But she is always logical, and tries hard to get the people to listen in a reasonable non-shouty way.
BTW walking away from an argument [which some people seem to think is a a sin] is wise in that house.
Farrah got the hump that first night because Natasha pointed out that she was a sore loser in the first task. The problem from the viewer POV is we didn't see Farrah's 'bad loser' reaction, we only saw Natasha talking about it.
I'm 100% sure, having seen Farrah through the rest of the series, that Natasha was 100% correct that Farrah WAS most definitely a sore loser and, for that reason Natasha had a reasonable, gut reaction, to send her into the tower.
They had to choose someone, and that's a good reason to choose when people don't know each other. First impressions was all they had to go on Farrah made a 'not good' one and Natasha said so.
Had we seen Farrah's bad loser reaction we'd agree with Natasha. BB didn't show it.