Comentario citado sobre Levítico 24:22

Even a baby that cannot live would be included. The Re’m says that this interpretation [saying that one is liable for killing a viable child] was received by Chazal as an oral tradition. Otherwise, we could say that “If one strikes a man” exempts killing a minor, and “any human being” makes one liable for killing an [adult who is a] woman, one whose gender is indistinguishable, or a hermaphrodite. The same applies to Chazal’s interpretation that the verse “If a man should strike” (Vayikra 24:17) makes one liable only for a blow that kills. Otherwise we could expound the opposite: since it says in our verse, “If one strikes a man and he dies,” this means only for a blow that kills. Therefore the verse in Vayikra says, “If a man should strike,” teaching that even for a blow that does not cause death, [still he would be liable]. The Re’m explained at length. However, it is difficult [how can Rashi suggest that one might be liable for the death penalty for killing even a baby that cannot live]. If so, when would one be liable merely to pay damages for killing a fetus [see v. 22]? An answer is: damages would apply when one had no intent to injure the fetus. This is similar to what Rebbi said (Sanhedrin 79a), that “A life for a life” (v. 23) means merely to pay money [when the striker intended to kill a certain person but actually killed another). Another answer is: One would be subject to the death penalty for killing an unviable baby that was already born, whereas before its birth, one would not be liable [to the death penalty, only to pay damages]. (Tosafos, Sanhedrin 84b)

Mishna I: One law for monetary cases and one law for capital cases in inquiry and investigation [i.e. cross-examination] of the witnesses, as it is said: “One justice shall be to ye” (Lev. 24:22). That is to say, all proceedings of justice must be unified.

The Talmud answers that conversion also cannot be done by the man himself, for he needs a court to convert and it is not clear that he will find three to serve for him in such a capacity.
Conversion is a legal matter (see Leviticus 24:22).
I should note that in earlier rabbinic literature it seems that conversion was a self-administered process. A person just decides to become Jewish, goes through the proper ritual and thereby becomes Jewish. Only later in the Talmudic period do we hear of the necessity for a court. I wrote an article about this—you can find it on academia.com if you are interested. And let me know what you think!