In his time period, Esperanto was conceived of as the international language because it was (by design) easy to learn, and drew its vocabulary from multiple (admittedly European) languages. He cites the example of someone in England (noting that he knew no English) being able to communicate with him... and the person who translated "An attempt into an International Language" into English sent a letter to a friend with an English-Esperanto dictionary... and received an Esperanto reply. It is very hard to do that with German.
The other point is that it doesn't belong to any country. When it was invented (1846, if I remember rightly) he was living in a culture where language was policed- he hailed from Russian-occupied Poland, and he grew up multilingual. He believed that a common, easy-to-learn, theoretically neutral language would help to facilitate greater understanding. If you are pleading via translator for someone to have the same views as you, with tears in your eyes, it simply fails to convey the same emotion- imagine that for yourself. However, when you are talking in Esperanto, a neutral language, then you can fully communicate exactly what you mean with one another.
You can imagine that racism would creep in to even the most gentle soul who heard someone speaking their own language in a flawed way- you can imagine how, unwittingly and even in a well-intentioned manner, they would disregard their views or not hold them in the same esteem. But all people (in theory) have equal access to Esperanto, and that makes it perfectly neutral.
English is a fine language, and my native tongue. I am not a "finvenkist" (someone who believes that Esperanto should be taught in schools and become widely spoken), but I believe that all the attempts to make something like English, French or Mandarin fall flat for these reasons- Esperanto, while not free from its problems, is devoid on many accounts of the same problems as one of the national languages that becomes international.
All of these arguments are not my beliefs, and this is the first time that I have articulated them, but they are the arguments made in favour of Esperanto by its creator. And I think they are sound.
I am an Esperantist- Mi estas Esperantano. (The term "Esperantisto" is common, but "Esperantisto" seems to mean someone who speaks Esperanto professionally, as the suffix "ist" is usually reserved for. Thus, I use "Esperantano" to describe someone who speaks Esperanto.)