This is a very important question.

1. Possibly we may give an answer based on the Pnei Yehoshua here (DH Min ha'Tefilin) who writes that he explained in the Mishnah that everyone agrees that women are exempt from Tefilin, because Tefilin is compared to learning Torah. When the Gemara says here that we might have thought that Tefilin are compared to Mezuzah, this is only a Chumra.

2. It seems that this means that the chief issue is what is compared to Talmud Torah. We know that Tefilin is similar to Talmud Torah, but since it might also be similar to Mezuzah women might also have been obligated. However, the Gemara concerning Mezuzah did not reference Tefilin because Tefilin is essentially similar to learning Torah, so if we would have said it is איתקש לתפילין this would anyway have been the same as saying it is compared to Torah.

3) I have just written a very brief answer for the moment, and it requires further thought. It is important to see the Gemara in Kidushin 34a, which is quite similar to our Gemara.

4) After thinking more clearly about this question, I would like to add the following:

a. To understand properly the Sugya here in Maseches Berachos, we must look also at the Sugya in Maseches Kidushin. The Mishnah in Kidushin (29a) states that women are exempt from all time-bound positive Mitzvos. The Gemara there (Kidushin 34a) derives this from Tefilin. Just as women are exempt from Tefilin, they are exempt from all time-bound positive Mitzvos. The Gemara continues that we know women are exempt from Tefilin because there is a comparison between Tefilin and learning Torah. In the same way that women are exempt from learning Torah, they are exempt from Tefilin.

The Gemara then asks, why do we not compare Tefilin to Mezuzah, so that women should be obligated to put on Tefilin, like they are obligated in Mezuzah? The Gemara answers that Tefilin are compared to Talmud Torah both in the first and second Parshah of Shema, while Tefilin are compared to Mezuzah only in the first Parshah. (This is because the Mitzvah of learning Torah interrupts between Tefilin and Mezuzah in the second Parshah of Shema.)

b. It seems that we now have a good reason for why the Gemara in Berachos 20b said that we might have thought that women are exempt from Mezuzah because Mezuzah is compared to Talmud Torah, rather than saying because Mezuzah is compared to Tefilin. This is because the root of the reason for why women are exempt from Tefilin is that they are exempt from Talmud Torah, as we see in both the first and second paragraphs of the Shema, where Tefilin are next to learning Torah. Therefore, if Berachos 20b would have said that we might have thought that women are exempt from Mezuzah because they are exempt from Tefilin, we would still have had to ask the question: how do we know that women are exempt from Tefilin, and the answer would have been because Tefilin are compared to Talmud Torah. Since the original source of Tefilin is from Talmud Torah, Berachos 20b referenced Talmud Torah.

5) Answer of the Tzelach:

a. I saw that the Tzelach (by the author of Noda bi'Yehudah), DH Sham uv'Mezuzah Peshita, writes that the reason why the Gemara references Talmud Torah is that there is a similarity between the Mitzvah of Mezuzah and the Mitzvah of learning Torah: they are both limited by time. This is why the Gemara preferred not to compare Mezuzah to Tefilin, because one is obligated in Tefilin only in the daytime and not on Shabbos, whereas one is always obligated in Mezuzah.

b. The Tzelach writes that it is possible that this is why Rashi (DH Nakish) writes "just as women are exempt from learning even though this Mitzvah is not limited by time, so women are exempt from Mezuzah." Rashi is hinting that Talmud Torah and Mezuzah possess a common factor -- they are both Mitzvas Aseh she'Ein ha'Zman Grama.

Kol Tuv,

Dovid Bloom