I'm not sure that there are halachic arguments per se, rather, there's an argument as to exactly what halacha is. The Talmud (Megila 23a) states that "all may go up to be included in the seven (aliyos) - even a child, even a woman but the rabbis said a woman may not (publicly) read from the Torah because of "kovod hatzibur" (the congregation's honor). The Shulchan Aruch (17th Century code of Jewish law - the key work of halacha for Orthodox Jews), definitively quotes that Talmud passage along with its "kovod hatzibur" clause. You won't find any exceptions to this treatment anywhere in the classical halachic literature. The halacha concerning women being counted in a minyan is even less ambiguous.
The question now is, 'what do we do with that information?' Orthodox Judaism believes in an open revelation at Mt. Sinai which included the information and legal mechanisms necessary to understand how Torah law (i.e., God's will) applies to a given situation. The Shulchan Aruch is, in our eyes, the voice of that revelation
Orthodoxy sees the Torah as a binding "constitution" given by God (a constitution that must be understood and applied, but not judged by subjective or arbitrary standards). So once we've determined the gist and intent of the Talmud and codes, that's the end of the story. That doesn't mean, though, that we can't try to understand a halacha: below, I've added a short discussion of one such possible rationalization.
In the meantime, however, let's contrast this with my (outsider's) understanding of Conservative Jewish theology. In their writings, Jack Wertheimer, Louis Jacobs and Ismar Schorsch all struggle with the problem of halacha and obligation. Halacha, in their eyes, is a process that has evolved from its original Mt. Sinai form (none of the above will openly admit that there actually was a special revelation by God of the Torah's text) - or, as Jacobs put it, "God didn't reveal himself the Jews, but rather, through the Jews." Halachic principles are, therefore, binding only through some subjective and changing mechanism (like 'communal consent,' in Schorsch's system). Something that's absolutely central to Judaism in one generation might, in their view, become a nice custom in the next and legitimately slip into complete obscurity a generation further on if only changing communal standards so decree.
Against that background, many Conservative Jews will look to halacha for ideas or inspiration, but their final arbiter is their own system of subjective values. Therefore, if local contemporary standards recommend egalitarian social units then these are the units into which the Conservative halacha must be squeezed. But then the clear conclusion of the Talmud and classic halachic literature is no longer considered binding or authoritative.
That, I think, is the key issue.
There is, however, one more question that might be worth considering: "what will God get from this?" Since the study of the Torah (which is, of course, the goal of public Torah reading) is a religious act created and required by God, we must be sure that the way we do it is actually the way God wants it done. And the halachic process is the only possible source of God's will of which I'm aware (at least, no Conservative Jew has ever offered me an alternative).
Now here's the explanation I promised above:
What, exactly, is meant by the Talmud with the words "the congregation's honor." Rabbi Akiva Eiger in Megila 24b appears to point out that the concept of kovod hatzibbur is used in a number of other contexts whose similarities are telling. The other examples of concern for kovod hatzibbur mentioned by Rabbi Eiger are
I admit that these comparisons require more research (Rabbi Akiva Eiger was characteristically brief), but I will suggest that each of the above problems involves subjecting a congregation to a process that lacks halachic necessity. Now, in the first two cases, the activity in question also imposes time delays on the public but nevertheless, the overall common denominator is that none of the activities is obligatory. A woman certainly doesn't share in halacha a full to be involved in the recitation of the Torah, so her participation here might also be understood as an optional, and therefore a "burden" on the community (even if there could exist simultaneously a positive side - as with the first three cases above).
- one doesn't roll a sefer Torah while the congregation is waiting (Yoma 70a)
- one doesn't uncover the box (taiva) temporarily containing a sefer Torah while the sefer is being returned to its permanent home in someone's house (as was the custom in the time of the Gemara - out of safety concerns) while the congregation is waiting (Sota 39b)
- one doesn't read publicly from a chumash (Gitin 60a)
- one doesn't allow a barefoot child to be called up to the Torah (Megila 24b)