Q:

Why would you use word embeddings to find similar words?

One of the applications of word embeddings (such as GloVe) is finding words of similar meaning. I just had a look at some embeddings produced by glove on large datasets and I found that the nearest neighbors of a given word are often fairly irrelevant. Eg. ‘dad’ is the closest neighbor of ‘mom’, ‘dealership’ is the seventh closest neighbor of ‘car’. 
In light of this, if you wanted to find words of similar semantics why would you prefer using embeddings instead of just downloading a database of synonyms from an online dictionary that is compiled by humans? 

A:

It depends on how similarity is defined. If similarity is defined as human-defined semantics, then a synset (i.e., synonym set) is most appropriate. If similarity is defined as frequent co-occurrence, then word embeddings are most appropriate. Even within semantic similarity, there are many approaches beyond synsets.
One advantage of word embeddings over synsets is the ability to automatically find similarity with multi-word term vocabulary. For example, the common word analogy - Man is to king as woman is to queen.

