I think you're asking the question the wrong way. As other commenters have pointed out, the level of linguistic diversity in Europe is not especially high compared to other parts of the world (for example, Africa has some 2,000 languages, with 250 of them spoken in Nigeria alone).

The real question is why there is so little linguistic diversity in a large country such as the United States. And the answer has to do with the fact that the country was created through colonialism: a diverse set of societies were swept aside and displaced by a wave of settlers who shared a common language and culture and were able to expand it quickly through the process of settlement.

You can see a similar dynamic with respect to the political boundaries of the United States and Canada (or Australia), which follow a regular checkerboard pattern, reflecting the use of rectangular methods of land measurement - which facilitated the quick distribution of tracts to settlers. Most other parts of the world have more irregular, idiosyncratic boundaries because they were not formed by settler colonialism.

(As a side note, I'd add that when it comes to counting languages there is some subjectivity - as the old saying goes, "A language is a dialect with an army and a navy.")

We had a similar question a couple days ago. The short answer is that there hasn't been a single empire or migration of people to spread a language around to the exclusion of others since the Migration Period in the early Middle Ages. That said, the vast majority of European languages are very closely related, either due to introduction of Germanic and Slavic languages during the Migration Period, or due to the expansion of the Roman Empire. There are some languages descended from earlier periods of Indo-European migration (like Celtic and Greek), and a few non-Indo-European languages that are either ancient (Basque) or due to relatively recent migrations (Hungarian).

If you were turn the clock back to around 1500, North America would have been considerably more linguistically diverse than Europe - which I discuss in detail in my post in the other question. Unfortunately, over the last 500 years a handful of European powers (or European-derived powers like the United States) have spread their European languages either through recent migrations of their own people through the continent or by actively suppressing Native languages.

Relatively small geographically to what?

I know I'm not including any sources in this answer but what is your comparison? North America?

Because a single country like India or China has multiple languages used in Asia and just as many different languages. Europe has different countries and therefore different languages.

North America is more of an outlier than Europe is

Its quite arguable that a common language did develop (or at least spread to attain dominance) in the form of Vulgar Latin in much of western Europe. However, languages tend to follow a pattern of dialect creation, which diverge into mutually unintelligible languages, which is how the modern Romance languages now exist. Other regions can be just as or more diverse in language, which for the purposes of comparison we can use South-East Asia. Europe is roughly 10 million square kilometres, with a population of roughly 750 million people. There are 3 main language groups, being Romance, Germanic and Slavic, all of which are within the Indo-European family and whom the vast majority of the population fit into. There are several other minor distinct languages, including the Celtic languages, Baltic languages and Greek, all of which are Indo-European, as well non-Indo-European ones such as the many Caucausian languages, Hungarian and Basques, but they are a numeric minority.

South-East Asia has a area of roughly 4.5 million square kilometres and a population of roughly 620 million people. Language-wise, the area has 5 main language families, distinct from one another. These are Tai-Kadai (various distinct Thai languages), Austronesian (Formosan languages, Malay, Javanese, Sundanese), Sino-Tibetan (Chinese, Burmese, Chin), Austroasiatic (Vietic languages, Khmer, Bahnaric languages) and Hmong-Mien (Hmong and Mien languages). Each one of these languages used as examples are extreme simplification of an incredibly controversial academic topic, which gives little sense of the incredible variety. Vietnam alone has 54 officially recognised ethnic groups, most of whom possess distinct languages. Its quite clear than that Europe is at least certainly not unique in possessing a variety of languages.