Answer: An ostrich
It always surprised me that the same word is used in Greek for ostrich and sparrow – στρουθός. Xenophon describes ostriches in the Arabian desert.
στρουθὸν δὲ οὐδεὶς ἔλαβεν: οἱ δὲ διώξαντες τῶν ἱππέων ταχὺ ἐπαύοντο: πολὺ γὰρ ἀπέσπα φεύγουσα, τοῖς μὲν ποσὶ δρόμῳ, ταῖς δὲ πτέρυξιν αἴρουσα, ὥσπερ ἱστίῳ χρωμένη.
No one caught an ostrich. Those who tried to chase them on horse soon stopped. For it pulled far ahead as it ran away by running with its feet and by raising its wings like a sail.
Xen. Anab. 1.5.3
Oppian explains the name – the ostrich is a cross between a sparrow and a camel.
ναὶ μὴν ἄλλο γένεθλον ἐμοῖς ἴδον ὀφθαλμοῖσιν
ἀμφίδυμον, μέγα θαῦμα, μετὰ στρουθοῖο κάμηλον:
And there is another double-natured animal I have seen with my own eyes, a great wonder, a camel combined with a sparrow.
Oppian Cynegetica 3.482
I am not sure how the original ostrich was born but I suspect that a male sparrow must have mated with a female camel rather than the other way around.
Once the species was created the they still had a peculiar way of reproducing. I have to say I don’t really understand the mechanism involved here.
οὐδὲ μὲν ὀρνίθεσσιν ὁμοίϊος ἀμβαδὸν εὐνή,
Βάκτριον οἷα δὲ φῦλον ἔχουσιν ἀπόστροφα λέκτρα:
Nor do they mate by mounting like other birds but like the Bactrian camel their mating is rear to rear.
Oppian Cynegetica 3.500
Usually the word sparrow when used for an ostrich was qualified as the great sparrow or the land sparrow or,as used by Xenophon above, given the female gender. Our word ostrich ultimately comes from strouthos, the Greek for sparrow or ostrich.