From the Disproofs of the Oral Law series.
Textual Proofs3. R. HaLevi further asks what the Torah means when it says [Exodus 12:2] "This month shall mark for you the beginning of the months"? To which months is this referring? Is it referring to Egyptian months (where the Jews were living at the time) or Chaldean months (from where their patriarch Abraham originated)? Solar months or lunar months? Without an oral tradition, there is no way to know to what this verse is referring [cf. R. Avraham Ibn Ezra, Commentary, Lev. 25:9; Rashbatz, ibid. This, by the way, seems to alleviate the issue of counting January as the first month. Since the verse is referring to lunar months, there is no prohibition to count January as the first solar month.].
1. To which months is this referring? Exodus 13:4 "Today you are going out, in the New-Moon of ripe-grain / abib". Also in Ex 23:15 and several other places.
Abib is a stage in the growth of barley, when it has almost ripened. We learn this by analyzing Exodus 9:31-32, which says: "Now the flax and the barley were stricken [by hail], for the barley was abib and the flax was giv'ol, but the wheat and the spelt were not stricken, because they were dark / afilot". This verse, with the knowledge of the development stages of grain, tells us when the month of abib is. Nehemia Gordon explains [local], in part,
The above passage relates that the barley crops were destroyed by the hail while the wheat and spelt were not damaged. To understand the reason for this we must look at how grain develops. When grains are early in their development they are flexible and have a dark green color. As they become ripe they take on a light yellowish hue and become more brittle. The reason that the barley was destroyed and the wheat was not is that the barley had reached the stage in its development called Abib and as a result had become brittle enough to be damaged by the hail. In contrast, the wheat and spelt were still early enough in their development, at a stage when they were flexible and not susceptible to being damaged by hail. The description of the wheat and spelt as "dark" (Afilot) indicates that they were still in the stage when they were deep green and had not yet begun to lighten into the light yellowish hue which characterizes ripe grains. In contrast, the barley had reached the stage of Abib at which time it was no longer "dark" and at this point it probably had begun to develop golden streaks.
The Bible tells us that the first month is the one in which grains reach a certain stage in their ripening, and it tells us what that stage is. We thus know when the first month is.
2. Solar or lunar? In Hebrew, the word chodesh, means both "month" and "new moon". A better translation of the verse in question, given by Everett Fox, might be "Let this New-Moon be for you the beginning of New-Moons, the beginning-one let it be for you of the New-Moons of the year".
The Tanakh speaks of new moons throughout. There is not a hint of solar months.* For two examples, see Numbers 10:10
And on your joyous occasions -- your fixed festivals and new moon days -- you shall sound the trumpets over your burnt offerings and your sacrifices of well-being. They shall be a reminder of you before your God: I, YHWH, am your God.
Or, Numbers 28:11 "On your new moons you shall present a burnt offering to YHWH: two bulls of the herd, one ram, and seven yearling lambs, without blemish".
How is it that there are celebrations on the new moon days, that "solar months" are not mentioned anywhere even once, if the months are solar?
* The only possibility I can think of is Genesis 7-8, in which 150 consequtive days could be seemingly equated with exactly 5 months. However, this issue can be resolved with lunar months.
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