Why did Pharaoh target Jewish male infants?

Summary: Philo and Josephus, with Josephus giving the famous midrash about astrology. What was bothering Josephus?

Post: In parashat Shemot, in Pharaoh's command to the midwives:

16. And he said, "When you deliver the Hebrew women, and you see on the birthstool, if it is a son, you shall put him to death, but if it is a daughter, she may live."

טז. וַיֹּאמֶר בְּיַלֶּדְכֶן אֶת הָעִבְרִיּוֹת וּרְאִיתֶן עַל הָאָבְנָיִם אִם בֵּן הוּא וַהֲמִתֶּן אֹתוֹ וְאִם בַּת הִיא וָחָיָה:

and later to the Egyptian nation:

22. And Pharaoh commanded all his people, saying, "Every son who is born you shall cast into the Nile, and every daughter you shall allow to live."

כב. וַיְצַו פַּרְעֹה לְכָל עַמּוֹ לֵאמֹר כָּל הַבֵּן הַיִּלּוֹד הַיְאֹרָה תַּשְׁלִיכֻהוּ וְכָל הַבַּת תְּחַיּוּן:

Why this targeting of the males? Two fairly early approaches. On, by Philo:

III. (8) And he was thought worthy of being bred up in the royal palace, the cause of which circumstance was as follows. The king of the country, inasmuch as the nation of the Hebrews kept continually increasing in numbers, fearing lest gradually the settlers should become more numerous than the original inhabitants, and being more powerful should set upon them and subdue them by force, and make themselves their masters, conceived the idea of destroying their strength by impious devices, and ordered that of all the children that were born the females only should be brought up (since a woman, by reason of the weakness of her nature, is disinclined to and unfitted for war), and that all the male children should be destroyed, that the population of their cities might not be increased, since a power which consists of a number of men is a fortress difficult to take and difficult to Destroy.

Thus, the initial concern was:

9. He said to his people, "Behold, the people of the children of Israel are more numerous and stronger than we are.		ט. וַיֹּאמֶר אֶל עַמּוֹ הִנֵּה עַם בְּנֵי יִשְׂרָאֵל רַב וְעָצוּם מִמֶּנּוּ:
10. Get ready, let us deal shrewdly with them, lest they increase, and a war befall us, and they join our enemies and depart from the land."		י. הָבָה נִתְחַכְּמָה לוֹ פֶּן יִרְבֶּה וְהָיָה כִּי תִקְרֶאנָה מִלְחָמָה וְנוֹסַף גַּם הוּא עַל שֹׂנְאֵינוּ וְנִלְחַם בָּנוּ וְעָלָה מִן הָאָרֶץ:

and only men would be expected rise up in war.

Josephus, meanwhile, relates what we know from the midrash, and from Rashi:
אם בן הוא וגו': 
לא היה מקפיד אלא על הזכרים, שאמרו לו אצטגניניו שעתיד להוולד בן המושיע אותם:

Josephus omits summarizing even the pasuk about concern for them rising up in war. For the reason for concern, he writes:

1. NOW it happened that the Egyptians grew delicate and lazy, as to pains-taking, and gave themselves up to other pleasures, and in particular to the love of gain. They also became very ill-affected towards the Hebrews, as touched with envy at their prosperity; for when they saw how the nation of the Israelites flourished, and were become eminent already in plenty of wealth, which they had acquired by their virtue and natural love of labor, they thought their increase was to their own detriment. And having, in length of time, forgotten the benefits they had received from Joseph, particularly the crown being now come into another family, they became very abusive to the Israelites, and contrived many ways of afflicting them; for they enjoined them to cut a great number of channels for the river, and to build walls for their cities and ramparts, that they might restrain the river, and hinder its waters from stagnating, upon its running over its own banks: they set them also to build pyramids, and by all this wore them out; and forced them to learn all sorts of mechanical arts, and to accustom themselves to hard labor. And four hundred years did they spend under these afflictions; for they strove one against the other which should get the mastery, the Egyptians desiring to destroy the Israelites by these labors, and the Israelites desiring to hold out to the end under them.

So why target only the males? He writes:

2. While the affairs of the Hebrews were in this condition, there was this occasion offered itself to the Egyptians, which made them more solicitous for the extinction of our nation. One of those sacred scribes, who are very sagacious in foretelling future events truly, told the king, that about this time there would a child be born to the Israelites, who, if he were reared, would bring the Egyptian dominion low, and would raise the Israelites; that he would excel all men in virtue, and obtain a glory that would be remembered through all ages. Which thing was so feared by the king, that, according to this man's opinion, he commanded that they should cast every male child, which was born to the Israelites, into the river, and destroy it; that besides this, the Egyptian midwives should watch the labors of the Hebrew women, and observe what is born, for those were the women who were enjoined to do the office of midwives to them; and by reason of their relation to the king, would not transgress his commands. He enjoined also, that if any parents should disobey him, and venture to save their male children alive, they and their families should be destroyed. This was a severe affliction indeed to those that suffered it, not only as they were deprived of their sons, and while they were the parents themselves, they were obliged to be subservient to the destruction of their own children, but as it was to be supposed to tend to the extirpation of their nation, while upon the destruction of their children, and their own gradual dissolution, the calamity would become very hard and inconsolable to them. And this was the ill state they were in. But no one can be too hard for the purpose of God, though he contrive ten thousand subtle devices for that end; for this child, whom the sacred scribe foretold, was brought up and concealed from the observers appointed by the king; and he that foretold him did not mistake in the consequences of his preservation, which were brought to pass after the manner following: -

What is bothering Josephus? I wonder if the selection of the midrash and ignoring of the pasuk was done deliberately. After all, Josephus is writing in the aftermath of the Judean revolt. Would he really want his Roman readership commiserating with Pharaoh and the Egyptians, and agreeing that the growing Jewish population might rise up and join their enemies? I don't think that would be very smart.