The Dag asks:

Why is Aphrodite considered an Olympian instead of a Titan?

Well.  Hesiod doesn’t give a definitive list of “the Olympians” in the Theogony, and it’s the Theogony that claims Aphrodite was born of the blood of Ouranos – Homer says in the Iliad that she’s a daughter of Zeus.  In fact, I don’t think anyone gives a definitive list of “the Olympians” until the Hellenistic period.  The Homeric Hymn to Hermes mentions that there are twelve of them, but doesn’t say which twelve, except that Hermes isn’t one of them (because the Hymn is about Hermes’ ascent to godhood).  The idea that there are twelve of them is persistent in ritual, but it doesn’t seem like anyone thought it was particularly important to come to a firm agreement about who the twelve actually were (Herodorus’ list of the twelve gods to whom Heracles made sacrifices at Olympia includes Kronos, Rheia and Alpheios, who would never make it onto any modern list of “the twelve Olympian gods”).  It’s also perfectly acceptable in Greek poetry to refer to a whole bunch of minor deities, notably the Muses, as “Olympian” (often it’s really just a synonym for “divine”).  So “Olympian” is fuzzy and you can get away with throwing a whole lot of people in there.

“Titan,” on the other hand, is pretty specific.  Hesiod claims that “Titan” was a name given to them by Ouranos, and he derives it from τιταίνω, to stretch or strain, and τίσις, vengeance (which is probably not the real etymology, but it’s what he believed, at any rate), so I think in his mind “Titans” only means the twelve children of Gaia and Ouranos who rebelled against the rule of their father, whom he explicitly lists: Kronos, Rhea, Koios, Phoebe, Hyperion, Theia, Iapetos, Mnemosyne, Kreios, Themis, Okeanos and Tethys.  There are other, different lists of the Titans given by other ancient authors (Apollodorus adds Dione, the mother of Aphrodite in the Homeric tradition, for a total of thirteen; the sixth Clementine Homily seems to think that Demeter was a Titan, but this is a Christian text citing pagan myth in order to discredit it, so it could conceivably have some details muddled).  Today we often consider several of their more famous children to be “Titans” as well – notably Atlas, Prometheus, Epimetheus, Leto, Helios, Selene and Hekate, or even more distant descendants like Calypso – but to be honest I can’t find an ancient source that actually calls any of them “Titans” so I’m not sure when that starts; it could be in the scholia or something.  So the short answer is simply that, despite belonging to an earlier generation than the other “Olympians” in Hesiod’s version of the creation myth, there is no tradition I’m aware of that ever says Aphrodite was part of the rebellion against Ouranos.  It also helps that Aphrodite literally lives on Olympus, which the Titans traditionally didn’t – according to Hesiod they hung out on Mount Othrys (which like Olympus is the name of a real mountain in Greece; it kind of faces Mount Olympus across the plain of Thessaly).