I realize that I am working on a nearly impossible task here. Trying to convince someone who thinks they don't want to watch The 100 that it's worth their time is incredibly difficult. What it seems to be from the outside is not what it is, but it spends just long enough as the bad version of itself to make most people stop watching it. When you do get through it, however, it is a kind of incredible little show that doesn't get nearly the love or conversation that it deserves. On a different network or with superficial genre changes, this would be a highly regarded show, but it's a Young Adult show on The CW, so people get a bad impression from the start.
Let's start there, looking at everything that is stacked against this show:
I'm going to not talk much about season 2. It is where the show knows exactly what it is and can do everything that it is capable of. It is also a minefield of possibly spoiling things and moments that are probably best unspoiled, so I will just say this: the show is at its absolute best in episodes 8 and 16 of season 2. What I can more comfortably talk about is in Season 1:
Not all of the show is great, and there are some weak points. There are a few that are generally agreed upon, but even then they are turned into parts of the story that are generally seen as a positive influence, if not outright positive themselves.
Brief footnote: Yes, I am aware of Devin Faraci's article on exactly this topic, which is a monumental case of bad timing. This was finished but not yet published before his article was, though now I'm really glad I cut my own Battlestar Galactica reference from the end of this article.