An Oracle sequence is generator for a guaranteed series of unique numbers which performs well and scales in a multi-user environment. The trade off for performance and scalability is that occasionally there are gaps in the series.
It is incredibly rare to find a use case where such gaps really matter to the organisation. Although it is tragically all too common for people to get into a needless frenzy about them.
Are there alternatives to sequences? Sure, we're always free to write our own code. Depending on your business needs it might be quite simple or it might be rather complicated.
The important things to bear in mind to bear in mind are performance and scalability. You are inevitably sacrificing a bit of both by choosing not to use a sequence. But writing your own series generator provides an opportunity to really muck things up.
So, understand the implications and be sure your boss is fully sold on the idea.