Species of what, insects?
According to this
list, only 40 have gone extinct in the last 100 years. 40 certainly is a high number, but you're saying tens of thousand species over the course of a couple decades.
all living things are split into 5 major kingdoms: animalia, plantae, fungi, protista, and monera.
if something from there dies then it counts as extinct.
sure, most people care more about a dolphin than some weird bug found in the amazonian rain forest or some amoeba found at the bottom of the sea.
obviously the number i've given is just an estimation. we can't say for sure how many species exist let alone how many die per day.
each year we discover 15-20 thousand new species and there's speculation we still have not discovered ~30 million species.
“In the beginning God said, the four-dimensional divergence of an antisymmetric, second rank tensor equals zero, and there was light, and it was good. And on the seventh day he rested.”- Michio Kaku