"The tax man" is used to refer to the government's internal revenue service and its employees collectively. In the US, this is the IRS. In the UK, this is HMRC. The internal revenue services of governments are responsible for collecting the tax from the citizens and businesses of the government's country, and bringing prosecution against tax evaders.
Taxes and tax collectors can be seen in a poor light by some people, who may believe that it is government-sponsored robbery and robbers, or any number of other similar crimes. In the New Testament, tax collectors are portrayed as greedy (and greed is a cardinal sin in Christianity).
By calling the character the tax man, it would appear to me that the character is being associated with something seen as bad (the internal revenue service), and therefore that character is bad and is guilty by association. The character may see it as a slight on their honour or integrity. By associating the character with the faceless internal revenue service, there may also be an element of dehumanization – insulting the character by separating them from their human traits.
However, by being called a tax man the character is not as closely associated with the internal revenue service. It may show a greater separation between the character and the character's job. It may allow this character to think that while their job may be bad, they are not themselves bad.
I assume that the person who called the character "the tax man" is a gas engineer of some sort. In which case, being called "the gas man" brings in the same dehumanization factor, and the character may be trying to show the gas engineer how it feels to be called "the tax man" by calling the gas engineer a similarly dehumanizing insult.