Why would Aphrodite be armed?
Pausanias tells us that the Spartans worshipped Aphrodite Hoplismeni (~armed) and Aphrodite Areia (~of Ares, warlike):
[Paus. 3.15.10] Not far from the theatre is a sanctuary of Poseidon God of Kin, and there are hero-shrines of Cleodaeus, son of Hyllus, and of Oebalus. The most famous of their sanctuaries of Asclepius has been built near Booneta, and on the left is the hero-shrine of Teleclus. I shall mention him again later in my history of Messenia. A little farther on is a small hill, on which is an ancient temple with a wooden image of Aphrodite armed. This is the only temple I know that has an upper storey built upon it.
[Paus. 3.17.5] On the left of the Lady of the Bronze House they have set up a sanctuary of the Muses, because the Lacedaemonians used to go out to fight, not to the sound of the trumpet, but to the music of the flute and the accompaniment of lyre and harp. Behind the Lady of the Bronze House is a temple of Aphrodite Areia (Warlike). The wooden images are as old as any in Greece.
[Paus. 3.23.1] Cythera lies opposite Boeae; to the promontory of Platanistus, the point where the island lies nearest to the mainland, it is a voyage of forty stades from a promontory on the mainland called Onugnathus. In Cythera is a port Scandeia on the coast, but the town Cythera is about ten stades inland from Scandeia. The sanctuary of Aphrodite Urania (the Heavenly) is most holy, and it is the most ancient of all the sanctuaries of Aphrodite among the Greeks. The goddess herself is represented by an armed image of wood.
Source: Pausanias. Pausanias Description of Greece with an English Translation by W.H.S. Jones, Litt.D., and H.A. Ormerod, M.A., in 4 Volumes. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1918
Why would the goddess of love, beauty, and procreation be armed? She wasn't exactly known for her military attributes. In fact, in Book 5 of the Iliad Zeus very bluntly dismisses her abilities as a warrior:
Of a surety now Cypris has been urging some one of the women of Achaea to follow after the Trojans, whom now she so wondrously loveth; and while stroking such a one of the fair-robed women of Achaea, she hath scratched upon her golden brooch her delicate hand.” So spake she, but the father of men and gods smiled, and calling to him golden Aphrodite, said: “Not unto thee, my child, are given works of war; nay, follow thou after the lovely works of marriage, and all these things shall be the business of swift Ares and Athene.”
Source: Homer. The Iliad with an English Translation by A.T. Murray, Ph.D. in two volumes. Cambridge, MA., Harvard University Press; London, William Heinemann, Ltd. 1924.
Was this militaristic version of Aphrodite a Lacedaemonian peculiarity? Could, perhaps, these images that are "are as old as any in Greece" be an allusion to Ishtar, an echo of Aphrodite's Mesopotamian origins?
Another fairly damned good question...Basically, you have to read CAREFULLY the Iliad and understand why Zeus is rebuking Aphrodite. While inspired by Ishtar episode in the tablet 6 of the Epic of Giglamesh it is just that: inspired; you should really see that Aphrodite is perfectly able to fight. will answer that later this day.
https://digitalt.uib.no/bitstream/handle/1956.2/2995/The%20transformations%20of%20the%20armed%20Aphrodite_Flemberg.pdf This essay might provide some answers.
This is an interesting paper, which suggests that either the statue of Aphrodite shows her holding her lover Ares' attributes, or that the artist wished to play with gender roles. (The Hellenistic fascination with the hermaphrodite is another such case.) Another paper, by Fritz Graf, focuses on the gender inversion, noting other rituals and images that involve women and arms, suggesting that such images and the rituals or stories behind them may represent an attempt to "think the unthinkable".
Why would the goddess of love, beauty, and procreation be armed? (Note, all the links are the same source.)
The cult of an armed Aphrodite was present in Laconia in early Archaic times. (PG2) The first images of Aphrodite were armed. (PG3) The first can be traced back to 380 B.C. But it is carried in a way that characterizes Aphrodite as a love goddess. (PG7) There are images of Aphrodite taking part in the Gigantomachy, but the source doesn't count this as prove that Aphrodite was a "war goddess." There are seventeen copies of a statue with Aphrodite putting on a sword ("This is clearly not a war goddess, but the love goddess donning the sword of Ares."). (PG4) The source says, "If the sculptor got the idea of creating an 'armed Aphrodite' from the old xoana, he created exactly the same thing as the poets, changing a war goddess into the familiar love goddess and thereby reestablishing the normal gender roles of society." (PG5) The source believes that Aphrodite was armed because it was warranted, possibly as a city goddess and not as a war goddess. (PG12)
To sum up, she was not originally seen as a war goddess. It is believed that before the Greek Pantheon as we know it came to be, Athena, Artemis and Aphrodite were one goddess. But, because a whole lot of males didn't like a goddess being so active/involved, split them up. Then, when a few of the older images cropped up, poets and artists reinterpreted them. (PG12-13)
Aphrodite is linked with Astarte, Near Eastern goddess of love and war. In Greece, her connection with war is through her affair with Ares. In one ancient sculpture, the Capuan Aphrodite, she may be holding Ares' shield, which in myth she took from him because she thought her reflection in it was so beautiful. She was also worshipped as Armed Aphrodite (Hoplitismenos) on AkroKorinth. A sculpture of her in Athens shows her with 1 bared breast, and a baldric and quiver for arrows. She would have held a bow in her left hand, now missing. Together, Aphrodite and Ares (Love and War), had a daughter, Harmonia (Harmony).