Giving a Hesped-Chabad custom and custom of other communities not to eulogize:
The Chabad custom is not to give any eulogies and so is the custom of other communities. One is to prevent eulogies from taking place for a deceased who belonged to a community who follows the above custom. Eulogies are not to be given for such a person even by people who are not accustomed to avoid eulogies, and even if the deceased was a Gadol Beyisrael. [Also what people call “parting words” is in truth a Hesped, and is not to be given.] After three days from the start of Shiva, one can eulogize the Niftar by saying stories and sayings regarding him.
 See Chikrei Minhagim 4:118 for a lengthy discussion on this subject
 Toras Menachem 1:3 “Chassidim do not say Hespedim”; Hosafos of Sichos Kodesh 5737 2:676 “You are to remain steadfast that a eulogy does not take place being that the deceased was a Lubavitcher” [This was a letter to Rav Shalom Rivkin, after his father Rav Moshe Dovber Rivkin, Rosh Yeshiva of Torah Vadaas, passed away; See Hapardes Kisleiv 5737 that in the end, due to this request, there were no Hespeidim, despite the attendance of all Gedolei Yisrael] Gesher Hachaim 1:13-4 [p. 84]; Letter of Chassid printed in Hagaon Melublin p. 19; The Rebbe Rayatz and Rebbe were not eulogized; The Toras Chesed was not eulogized [Hagaon Melublin p. 97] Rav Shmaryahu Noach of Babrosik was not eulogized as is the Minhag Chassidim. [Sefer Zichron of Rav Binyamin Goredetzky]; See Sefer Chikrei Minhagim 4:118; Nitei Gavriel 51 footnote 21
 See Aruch Hashulchan 344:7 and 14 that the giving of eulogies has become very scarce, and is no longer done in any community with exception to Lita and Zamut; Custom of Rupshitz, Ruzhin, Chernobyl, Viznitz, Gur [brought in Nitei Gavriel ibid]
The reason: a) As if one over exaggerates the praise of the Niftar, it is actually detrimental for his soul, as brought in Michaber 344:1. [Gesher Hachaim ibid; Kuntrus Hayachlieli 15:35] b) As people don’t know how to properly eulogize. [Aruch Hashulchan ibid] c) Due to Ayin Hara that may befall the person if his good deeds are revealed. [Kuntrus Hayachlieli 15:35] d) Not being eulogized properly is a merit for the deceased. [Kuntrus Hayachlieli 15:35] e) It may cause a Kitrug on the Jewish people, as someone may foolishly say that he died in exchange for an evil decree upon Klal Yisrael. [Kuntrus Hayachlieli 15:35] f) It is a Mitzvah to bury the deceased right away, as the soul cannot continue with its journey, either in Gan Eden or as a Gilgul, until the body is buried. Therefore, eulogies are not given in order not to delay the burial. [Chikrei Minhagim 4:118]
 See Hosafos of Sichos Kodesh 5737 2:676 that “You are to remain steadfast that a eulogy does not take place being that the deceased was a Lubavitcher”
 See Sichos Kodesh ibid and all sources ibid
 Pashut; See Sefer Chikrei Minhagim 4:118
 Toras Menachem 1:3 that so did the Rebbe after the passing of the Rebbe Rayatz.