The Gemara Yevamos (62b) records
שנים עשר אלף זוגים תלמידים היו לו לרבי עקיבא מגבת עד אנטיפרס וכולן מתו בפרק אחד מפני שלא נהגו כבוד זה לזה - Rabbi Akiva had twelve thousand pairs of students in an area of land that stretched from Gevat to Antipatris in Judea, and they all died in one period of time, because they did not treat each other with respect.
The Midrash Bereishis Rabbah (61:3) writes
אָמַר לָהֶם בָּנַי, הָרִאשׁוֹנִים לֹא מֵתוּ אֶלָּא שֶׁהָיְתָה עֵינֵיהֶם צָרָה אֵלּוּ לְאֵלּוּ תְּנוּ דַּעְתְּכֶם שֶׁלֹא תַעֲשׂוּ כְמַעֲשֵׂיהֶם - Rebbi Akiva told his new students, "My sons, the first ones only died because they had a narrow perspective with one another, but you should focus your attention not to do as they did."
which seems to parallel a very similar Midrash Koheles Rabba (11:6) here
אָמַר לָהֶם הָרִאשׁוֹנִים לֹא מֵתוּ אֶלָּא מִפְּנֵי שֶׁהָיְתָה עֵינֵיהֶם צָרָה בַּתּוֹרָה זֶה לָזֶה, אַתֶּם לֹא תִהְיוּ כֵן - Rebbi Akiva told his students, "The first ones only died because they had a narrow perspective with one another in Torah, but you should not do that."
Recognizing that these are individuals on a lofty level who were Rebbi Akiva's students, what precisely does "not respecting" each other mean?
(i.e. Were they insulting one another? Making fun of their chavrusah's pshat in learning? I once heard they continued respecting each other as they always did, but after everyone grew to great levels that initial respect was found to be lacking, but I'm looking for any sourced answer identifying what the students were actually doing)