Because it is descended from Sanskrit which has been known to be an Indo-European language since the very beginning of comparative linguistics.

It is genetically unrelated to Dravidian languages, but it does have a lot of Dravidian loanwords.

Kannada is very influenced by Sanskrit, but still is a Dravidian lang. Is there more Sanskrit influence in Sinhala compared with Kannada?

I speak and read Sinhala fluently. I can't speak to origins, but one thing that struck me the first time I learned a little Latin was the similarities:

queen: latin = regina. sinhala = regina.

tooth: latin = dente. sinhala = danta.

nose: latin = nasus. sinhala = naasa.

Etc.

It's more about linguistic structure than origin of words.

Kannada, Telugu & Malayalam, even pre-dravidan-movement Tamil have lot of borrowed sanskrit vocabulary, but they retain structure of Dravidian languages.

Also most common words used are also Dravidan origin.

For example:

Kannada - Naanu, Tamil - Naan, Telugu - Nenu, Malayalam - Njan

Etc..

Another small thing unique about Dravidian languages is clusivity, there's exclusive 'we' and inclusive 'we'. While modern Kannada, unlike Tamil / Telugu, doesn't retain this feature, some dialects such as Havyaka retain this feature.

Yes, but does Sinhala hase the linguistic structure of Dravidian languages or not?

Sinhala does not have the structure of Dravidian languages. However, the alphabet used to write Sinhala has a shared origin with the alphabets used to write Dravidian languages. Also due to long coexistence with Tamil in the island, Sinhala burrows lot of loanwords from Tamil.

I am Sinhalese who grew up in Sri Lanka. As such I am exposed to Tamil, but when I watch Tamil TV, at best I can pick few words here and there. But when I watch Hindi show, I understand a lot more due to the structure is very similar to that of Sinhala.

I don't understand sinhala but if it is classified as Indo Aryan language and not Dravidian, then that is the reason.

There will be always be some influence and loanwords from neighbouring languages but comparative linguistics can tell origin / family of the language pretty accurately.

Yeah, historical linguistics distinguishes between a language being influenced by another vs. descending from another.

For example, English is descended from Old English (a Germanic language), but was very heavily influenced by French (a Romance language, i.e. descended from Latin). The grammatical structure and origin of basic words are still more Germanic than Romance.

Languages are classified based on relatedness, not geography. Just as you have an Indo-Aryan language, Sinhala, that made it down to Sri Lanka, you also have a Dravidian language, Brahui, that stuck around up in Pakistan.

The famous example of an "out of place" language is Madagascar, where they speak a language you'd expect to find spoken by Pacific islanders.

Not OP, but Sinhala is classified as Indo-Aryan having developed when Buddhism spread to Srilanka and separate from Dravidian family of languages which is mostly limited to Southern part of India

Some tales tell that Sinhalese were Buddhists from somewhere near modern day Bengal who fled to avoid persecution.