Well I think I should be able to answer this.
I've been a strict alternator for quite a while, and it really helps to 'feel the beat" if that makes sense. I'd recommend playing easier maps with a very distinct and clear rhythm. Learn those pretty well and move onto more complicated rhythms. But make sure you keep track of your accuracy and your combo, and try to improve those. In time you'll be able to alternate. As for me, it just came naturally (because I couldn't play faster maps so I was forced to alternate to pass anything)
A lot of people are known as "single tappers" in which they primarily use one button to hit a lot of patterns. They'll use the other for quick doubles, triples, bursts, or streams. But rarely use it for other reasons.