I'm taking a 3-week Bio I summer course, and my textbook says the cell is the smallest/basic unit of life. I asked my professor why organelles aren't a living unit, and her reply was that they aren't self-sufficient. But it seems that cells in multi-cellular organisms need other cells with different specializations in order to survive. You can't just (or can't always) pluck a cell out of a larger organism and leave it to fend for itself outside of it. Same with an organelle. She said only the entire cell fits all the requirements for life, referring me to the textbook, but I couldn't find an actual description of these requirements. So, what is the relevant difference between an organelle and a cell such that only the entire cell is considered alive?
The definition of life is a controversy in itself, and as it is simply a word that can be understood by everyone however they wish, there is no "correct" definition. It is thus not really possible to give a "correct" answer to your question, but here are a list of things you may want to consider:
Mitochondria and plastids make a complicated exception to these, as they are originally derived from bacteria themselves. It is indeed debatable whether they could be considered alive, as they possess DNA and it is replicated in order for them to divide, like individual cells do. However, the machinery required is not produced by themselves but rather by their "host" cell, making them subject of a similar argument as viruses.