Not to be dressed sloppy:
One is to dress and look decent in order so he does not appear degrading in the eyes of others. This especially applies to a Torah scholar, or individuals who represents Torah in the eyes of others. [The Rebbe once instructed his Shluchim to Eretz Yisrael that they are to place due effort in the look of their dress, so they look respectable as fitting for their mission. The Rebbe Rashab once instructed the students of Tomchei Temimim to not wear their Tzitzis on top of their clothing, but rather under it, as it looked very sloppy in his eyes.]
Wearing the shirt tucked into one’s pants versus sticking out:
Wearing a dress shirt out of one’s dress pants is viewed by many in society as a sloppy way of dress and is hence not to be done, especially by those who appear as representatives of Torah. Despite the above, some are particular to wear their shirt out of their pants under one claim or another. Practically, these claims do not have any real basis, and certainly not of the caliber to negate the above said law, which requires a Jew who represents Torah to be dressed appropriately. Thus, one is to wear his shirt tucked in his pants and not look sloppy. Furthermore, wearing one’s shirt tucked in has the advantage of keeping one’s Tzitzis in place and prevents it from folding.
The custom in Lubavitch: The original custom in Tomchei Temimim of Lubavitch was to wear the Tzitzis on top of the clothing. However, after the Rebbe Rashab negated this practice [see above] the custom became to wear a long jacket, which would thus cover the Tzitzis. Later the custom became to wear short jackets and tuck the shirts inside the pants. It is only in more recent years that some Bochurim became accustomed to wearing the shirt out. As stated above, this should not be done and Bochurim are to look representable and tuck their shirts into their pants.
 See Kama 2:2 and Basra 2:3 and Michaber 2:3 [regarding wearing shirt inside out]; 53:32 [regarding the clothing of a Chazan]; Shabbos 114b “Any Torah scholar who wears a stained garment is liable for death as the verse states Kol Misaneiy Ahavu Maves” [see there also regarding wearing shirt inside out]; Kitzur Shulchan Aruch 3; Ketzos Hashulchan 3:3
 The reason: As otherwise he will be included within “All my haters love death” [Mishleiy 8:36], as people will say “how degrading Torah learners are”. [Kama ibid; Basra ibid; Perisha 2:3; Shabbos ibid; See also Admur 53:32] It is thus to be done in order not to be included within “My haters” Chas Veshalom. [Basra ibid]
 Sicha said on Night of Gimel Tamuz 1956 to the Shluchim to Eretz Yisrael
 The following was related by Rav Eli Landa Shlita, Rosh Hayeshiva of Tomchei Temimim Kfar Chabad [Free translation]: “The following story occurred in the city of Lubavitch. The Bochurim in Tomchei Temimim would wear their Tzitzis on top of their shirts [similar to the custom today of other Chassidic groups]. One day, the Rebbe Rashab told his son the Rebbe Rayatz, who was the official director of the Yeshiva, that upon looking out the window he saw the Bochurim Shleping their Tzitzis which was flying in all directions, and he does not like this at all. The Rebbe Rashab then said that the Bochurim should do one of the two; either to wear a long coat to cover the Tzitzis, or to tuck the Tallis Katan under their shirt. The Bochurim understood that the Rebbe Rashab preferred the first option and hence from that day and onwards the Bochurim in Lubavitch wore long coats.”
 Heard from Rav Eli Landa Shlita, Rosh Hayeshiva of Tomchei Temimim Kfar Chabad, and son of the famous Gaon and Chassid Rav Yaakov Landau Zatzal; Rav Leibal Groner replied to the author that he did not hear anything either way from the Rebbe on the above said subject; It is said of Rav Gringlass that he would tell the Bochurikm to tuck in their shirts
 Some claim to do so as so is the Chabad custom. Others claim to do so as the Rebbe was once witnessed in his private study to wear his shirt out of his pants. Others do so as they claim that it helps them with their Tzitzis so it does not fold. See next for the negation of these claims.
 Regarding the first claim: This is only a recent development in Lubavitch and was not the original custom in Tomchei Temimim. Regarding the second claim: The Rebbe was never seen in public with his shirt sticking out, as he always wore a closed Kapata covering it. Even if true that the Rebbe was once witnessed with his shirt sticking out, it was in his private study when his Kapata was off, and obviously cannot serve as any precedent for Bochurim today to wear the shirts out in public. Regarding the third claim: It is simply incorrect, as the Tzitzis are more guarded from folding if they are tucked in. Likewise, the “Gumi” elastic is worn by many for this purpose. Rav Eli Landa and Rav Leibal Groner likewise negated this latter point
 Related by Rav Eli Landa Shlita
 So was the custom in Tomchei Temimim in Eretz Yisrael at the time of Rav Landa’s attendance.