Why does it say that they could not speak with him "l'Shalom"?
Rashi: In praise of Yosef's brothers, inasmuch as they were not two-faced, pretending to be his friends when in fact, they hated him.
Seforno: Although they had to communicate with him in his capacity as manager of their father's estate (refer to 37:3:4:2), they could not bring themselves to talk to him in a brotherly manner.
Kol Eliyahu: One blesses someone who leaves "Go l'Shalom," and not "b'Shalom" (which is a bad sign - Berachos 64a). Because they hated him, they could not say the word 'l'Shalom.'
Ohr ha'Chayim: Normally, they would have argued with him and rebuked him, and their envy would depart. However, they saw that Yaakov loves him more than all of them together, and he publicized this through the robe. Now, they cannot debate with him to make Shalom, for Yaakov vindicated him (Yosef can 'prove' that he is right)!
Malbim: Normally, words of Shalom assuage hatred. However, hatred based on envy and thinking that he is a Rasha lying in ambush, when he [appears to] speak peaceably, this increases the hatred.
Ha'amek Davar: They could not bear his words of Shalom, for they thought that also he hates them, but hides his hatred. "Yachlu" is from Yachil, a measure; they did not have enough tolerance.
What was the root of the brothers' hatred for Yosef?
Ohr Yechezkel (Darchei ha'Avodah, p.36): It was not simple hatred of brothers. Everything is in Hashem's hands. 1 We find that right after they sold Yosef, they regretted this and wanted to return him!
Oznayim la'Torah: Now that Yaakov actually displayed his favoritism of Yosef, the brothers were afraid that, like Avraham, who gave everything he had to Yitzchak and sent the sons of his concubines away from Yitzchak, 2 he too, would give everything he had to Yosef and send them 3 away.
Ramban, Ha'amek Davar: Bnei Bilhah and Zilpah hated him for his Leshon ha'Ra about them. Bnei Leah hated him due to envy that Yaakov loved him more.
Malbim: They knew that of Avraham's sons, only Yitzchak was chosen, and of Yitzchak's sons, only Yaakov. They saw that Yaakov loves only Yosef, they feared that he sees Yosef as primary, and the rest of them are the shell. The robe supported this; it designates him for Avodas Hashem, like Bigdei Kehunah, He spoke Leshon ha'Ra to sully them in his father's eyes. His dreams showed that he wanted also kingship!
Bereishis Rabah (84:18), regarding the sale, expounds "Lamah Sas'enu Hashem mi'Derachecha [Takshi'ach Libenu mi'Yirasecha; Shuv... Shivtei Nachalasecha]" (Yeshayahu 63:17) - When You wanted, You put in their hearts to love. And when You wanted, You put in their hearts to hate.
See Bereishis 25:6.
Oznayim la'Torah: A fear that would affect the sons of Bilhah and Zilpah even more deeply than the sons of Leah.
QUESTIONS ON RASHI
Rashi writes: "Dabero - [I.e. they could not] speak with him [peacefully]." What is Rashi explaining?
Gur Aryeh: Do not translate as , '[they could not] speak of Yosef (i.e. about Yosef).' The subject of the verb 'Diber' is speech itself, not the content being conveyed. 1 Therefore, Rashi translates as, 'they could not speak unto Yosef,' i.e. with Yosef.
As Rav Hartman notes (in the Mechon Yerushalayim edition) - Compare to Gur Aryeh to 24:7 (refer to 24:7:4.1:1).