Why is it customary to call people with doctoral degrees doctors but not people with masters degrees masters? They are both graduate degrees that supersede the undergraduate degree.
If you're talking about the use of doctor as a title, as in "Dr. Smith", I doubt there's any compelling explanation. Most degrees don't come with titles: nobody say Master Smith or Bachelor Smith or Associate Smith. Historically, magister (corresponding to the master's degree) was just as appropriate a Latin title as doctor was, but it simply isn't used in modern English. These titles are nearly gone, with just one remaining. It's probably no coincidence that the last remaining title is also the fanciest, but that's just speculation.
Even for the doctorate, the use of the term "doctor" has degenerated to the point where in English it can only be used as a title, and not as a general noun. If you say "my friend John Smith is a doctor", practically everyone will assume he's a medical doctor. You could only get away with the more general usage in the narrowest academic context, and even there it would be considered pretentious and archaic.
In some countries the custom is different.
In the Czech Republic, Europe, where I come from, it still is generally customary to call masters masters. The title is different (magister, ingenieur*, or doctor**) but is more or less equivalent to the American master. And yes, it makes it easier to study for the sole purpose of being called
In neigbouring Germany, however, only doctors with degree equivalent to PhD. are titled by degree.
*) Not to be confused with engineer, the ingenieur degree means roughly master of engineering.
**) To add to the confusion, doctor degree can mean various degrees of a degree, not all of them being equal to PhD.
Update for clarification
Magister, ingenieur, and doctor are called magistr, inženýr and doktor, respectively, in Czech. The names come from Latin which is still used widely in Czech academia (where applicable). The respective abbreviations are Mgr, Ing and Dr. Thank you, Emil Jeřábek, for bringing this up.
The situation in Austria is similar to what Pavel Petrman describes. We do like our titles a lot.
Although nowadays almost all studies follow the Bachelor/Master system, as an engineering/science graduate one is still allowed to use the traditional title "Diplomingineur", usually abbreviated as "Dipl-Ing", instead of a title indicating the Master's degree. This is done mostly because it has a very high reputation in Austria and other German speaking countries. So once I graduate, I will be allowed to either call myself "mort, MSc" or "Dipl-Ing mort". However, calling myself "Dipl-Ing mort, MSc", which is sort of a wet dream for every title lover, is not allowed (but you do see it sometimes).
The equivalent for non-engineering/science studies was the title "Magister". However, graduates of those studies are only allowed to use their Master's degree (typically a Master of Arts degree), as was the original intention when switching to the Bachelor/Master system.
In regard to titles, Austria has a lot more anachronisms. For example, the title "Hofrat" is still in use, it usually comes with a high-ranking government job (it's not an academic degree). The title comes from the good old times when Austria was an Empire: "Rat"¹ means advisor, "Hof" designates the imperial court, so Hofrat literally means "advisor of the imperial court". Although Austria is a Republic for 70 years now, the title is still in use.
So think that's a bit crazy? Well. You can also combine academic and other titles. So a high-ranking government official might feel that he should only be addressed as "Herr Hofrat Dr. Huber". His wife, although not having earned any titles herself, might call herself "Frau Hofrat Huber".
Like I said, we do like our titles.
¹ Pronounced on the "a", not like the English "rat".
Historically, in the US, titles are not emphasized. Part of this has to do with the history of the US rejecting royal authority (ie, knighthood and family/land titles). Another aspect, though, is that academia is already considered pretentious to some degree, and requesting others address you according to your educational title in all social situations won't endear you to others, instead it sets up an unequal relationship.
Today, however, so many people have bachelors (30% of the US) and even masters degrees that it makes little sense to call out your achievement, when so many others around you have attained the same degree. PhDs are still relatively rare.
Lastly, note that it's largely within academia that the title is used on a regular basis - where even more people have bachelors and masters degrees. Usually one addresses their teacher with a title in many cultures (先生 in Japan, for instance). In the US, it's "professor" or "doctor", and usually professor is preferred.
The reality, though, is that other than medical doctors and outside academia, few PhDs that I'm aware of want or expect others to use their title. Demanding someone use a title when they address you is often seen as arrogance.
This question sounds like you can go around calling people doctor [name] outside an academic environment. I don't think that's true in English-speaking countries. When I got engaged to my wife (US born and raised), her mother was so excited that she was going to marry someone with a PhD that she started introducing me to the extended family as my future son-in law, Dr. Koldito. Literally everybody who heard her introducing me like that thought she meant I was a medical doctor.
So, I don't think there is anything weird in not being able to call people master [name]. You just can't use academic titles outside academia.
Technically the proper term of respect for an individual with a master's degree is "Mister". I think this usage is similar to that in the Royal Navy, where a ship's master would normally be referred to as mister, as in "Mr. Brown". Common usage has long ago eroded any significance that the title may once have had.