Why do Spanish and Greek sound so similar?

OP is right, and Joseph Boyle gets it, while Yiannis Tsiolis and Eve Vavilis are in fact being misled by already knowing Greek. (Ditto Laura Hale for already knowing Spanish, porque tiene una mujer española).

The question can’t be answered by someone who already knows Greek;* they’ll be looking for words they recognise (as did Laura); which is not the point. The question is not about similar words, it is only about the languages sounding similar.

(*OK, I don’t know Spanish as well as Greek, though I did hear a lot of Univision while living in SoCal. But I’m a linguist! Yay me.)

To someone who knows neither language, Greek and Spanish will indeed sound similar, for the reasons Joseph gave: [θ] and [ð] (although that’s not what jumps out as a similarity to me), the same vowels, lack of long-short vowel contrast, open syllables including words mostly ending in vowels, n, or r.

It’s really the vowels and syllable structure that does it. The structure fits Esperanto quite well, which is why some Esperantists recommend Greek/Spanish as the model to follow; and others resent them, as encouraging a rat-tat-tat rapid fire pronunciation, because they lack long vowels.

The intonation is probably going to be completely different; you won’t mistake a Mexican for a Cretan. But if you pick not-too-sing-song accents in each language, and turn the volume down so you can’t make out the words too clearly, yeah, they do sound alike.