Why make a two dollar bill?

The United States two dollar bill was created shortly after the US Civil War to facilitate commerce (same as all other denominations of currency) and to help with making change by filling the large gap between the one dollar coin/one dollar bill and the five dollar bill. It's the same mathematical reason there are $20 bills in between $10 and $50.

The US is extremely unusual among major countries in that it does not have a widely-circulating $2 coin or bill. The denomination is very common in most of the rest of the world, e.g. Canada, Australia, New Zealand, the EU, and the UK. Supposedly much of the reluctance comes from the fact that in the pre-inflationary days of the late 19th century, $2 was the going rate at race tracks and brothels. Many people were reluctant to spend the denomination out of concern that others would think they'd been visiting those improper venues. Today, reduced usage leads many people to erroneously believe the bills are rare so they hoard any they get, further reducing the number in circulation. In reality there are hundreds of millions of $2 bills in circulation but even that huge number is only about 1% of all bills. That makes them uncommon but definitely not rare.