Semitic Languages: Why do feminine-looking numbers agree with masculine nouns and vice versa in Hebrew and Arabic?

Great job on noticing. As an Arabic speaker (originally from Damascus), I can tell you that it's simply a grammatical rule. The numbers from 3-10 always have the opposite gender of the noun they're describing (in fus-Ha Arabic), as you pointed out. From examining my own Damascus vernacular (the accent, not fus-Ha), I simply always use the masculine despite the noun's gender. All accents are different, but the rule has slipped out of at least some of them. I do not speak Hebrew, but since it's a similar and closely related Semitic language, I wouldn't be surprised if it also had that grammar rule. I'm not sure if you can read Arabic or not, but for more information, here's a great site describing Arabic number usage: http://www.reefnet.gov.sy/education/kafaf/Bohoth/AdadMadoud.htm As for the last few remaining questions, I'm not sure. You could probably research the other languages to find out if there are similar cases, but that could be time consuming.

As noted by Hussein Aboubakr, this odd example of gender polarity exists in several Semitic languages, though it's largely disappeared from modern Arabic dialects (apparently it lasted longest in the Omani and Kuwaiti dialects) and is frequently ignored/gotten wrong in spoken Modern Hebrew. Amusingly, the only attempted explanation I've found online is by a linguistics enthusiast as part of his alternative history website http://www.veche.net/, which discusses a fictional Semitic language called Alashian: Proto-Semitic cardinal numerals, however, require additional explanation. These numerals *ħad- “one” behaved as a normal adjective, and occasionally *θin- “two” could as well. However, higher numerals (as well as optionally “two”) tended instead to appear as the head of a nominal construct; a form such as *ślāθu ʔinθāti “three women” more literally could be interpreted as “a trio of woman”. Consequently, the numerals often acquired the abstract feminine suffix *-t, yielding forms such as *ślāθtu ʔinšī(m) “three men”. At some point this suffixed numeral became generalized to masculine nouns, while feminine nouns continued using the original unsuffixed form. This is the origin of the so-called gender polarity seen in numerals in many ancient languages, where masculine nouns appear to be modified by feminine numerals and feminine nouns appear to be modified by masculine numerals.

When I learned Hebrew, as a ten-year-old, I explained this to myself, as a budding linguist, as a kind "conservation of prefixes" law (similar to the conservation of energy law in physics) that applies in English, as well: The cat walks regally. The cats walk regally. I've since suggested that principle as a mnemonic for people learning either language, and they've found it quite useful.

If you read Italian you can check this out: Brugnatelli, Vermondo. 1982. Questioni di morfologia e sintassi dei numerali cardinali semitici (Pubblicazzioni della Faccoltà di Lettere e Filosofia dell’Università di Milano 93. Sezione a cura dell’Istituto. di Glottologia 7) Firenze: La nuova Italia editrice. it explaıns 12 dıfferent theories regarding this. Basically I might be wrong but last I checkeed no one knows which is the real reason.It is important to note though that the very technical latin term used for this ("chiastic concord") is also the term used for a literary device in the bible that is a sort of structure where two pharses parallel each other in reverse order,  for ınstance "השופך דם האדם, באדם דמו יישפך" (if I were to keep a close to hebrew word and morphonolgy order the phrase would loosely translate as: 'the spiller blood (of) the (hu)man in the (hu)man his blood will be spilled').