וַיֹּ֨אמֶר אַבְרָ֜ם אֶל־ל֗וֹט אַל־נָ֨א תְהִ֤י מְרִיבָה֙ בֵּינִ֣י וּבֵינֶ֔ךָ וּבֵ֥ין רֹעַ֖י וּבֵ֣ין רֹעֶ֑יךָ כִּֽי־אֲנָשִׁ֥ים אַחִ֖ים אֲנָֽחְנוּ
Simple pshat I think is that Avraham was saying that since we are "anashim achim," there shouldn't be a fight. As haKsav v'haKabbalah writes: מצד קרבת משפחה ראוי קרבת הדעת ואהבה זה לזה לא פירוד הלבבות ומריבה
Netziv comments further on והכנעני והפרזי אז ישב בארץ that והנה המה יושבים בלא ריב ומחלוקת, ובין אברהם ולוט יש ריב, ויהא חילול השם לומר דאמונת אברהם אבינו מביאה לזה. The Canaani and Prizi managed to live peacefully alongside each other in the same land, so how does it look when Avraham and Lot, the Jews, can't live together without fighting? A chilul Hashem!
Malbi"m, however, explains that כִּֽי־אֲנָשִׁ֥ים אַחִ֖ים אֲנָֽחְנוּ is part of the explanation of why there IS a fight. Avraham was saying that had it been anyone else, they would not even be living in close proximity. It's because he and Lot are related, are close, that they are living on top of each other, and that is causing problems.
IIRC, the Maharal writes (can't recall offhand where, maybe someone will remind me) that the reason Klal Yisrael has so many internal quarrals is because we are more "sichli" than other people. Ideas and opinions matter to us. It's not a bug, it's a feature.
The Malbi"m perhaps would say that the reason we have no many internal quarrels is because Klal Yisrael has such a strong sense of "achvah." It too is a feature, not a bug. If you don't feel any connection with your neighbor, so you go your way and they go their way. The Canaani don't care that deeply what the Prizi think or do; the Prizi don't care really deeply about their Canaani neighbors. They do the polite wave when they see each other, some small conversation about the weather and whose turn it is to mow the lawn, but they are not getting together to discuss the meaning of life. But with us it's not like that. Because we feel like brothers and sisters, it matters more deeply to us what our neighbor, what the person who sits next to us in shul, is doing or thinking. That achvah is the motivation for us to go the extra mile when a Jew is in need, but sometimes it can lead us to get too involved where we shouldn't be.
In the next chapter, where we have the war between the 4 kings and the 5 kings, look at the different ways Lot is described in the following three pesukim:
1) וַיִּקְח֨וּ אֶת־ל֧וֹט וְאֶת־רְכֻשׁ֛וֹ בֶּן־אֲחִ֥י אַבְרָ֖ם וַיֵּלֵ֑כוּ וְה֥וּא יֹשֵׁ֖ב בִּסְדֹֽם
Lot is described as a nephew -- related, but not too closely. They aimed to capture him because, as Seforno writes, מפני שהיה בן אחי אברם שידעו עשרו, והיו מצפים שיפדהו אברם בהון רב, a rich man like Avraham would pay a price to redeem him.
2) וַיָּבֹא֙ הַפָּלִ֔יט וַיַּגֵּ֖ד לְאַבְרָ֣ם הָעִבְרִ֑י
Here Avraham is called Ivri. The "palit" is informing him of Lot's capture not because the "palit" knows they are related, but simply because he recognizes that Lot and Avraham came from the same area, the same side of the river. Or as Seforno writes לא שידע הפליט שיהיה אברם קרוב ללוט, רק ידע שהיה מחזיק בדעות עבר כמוהו.
3) וַיִּשְׁמַ֣ע אַבְרָ֔ם כִּ֥י נִשְׁבָּ֖ה אָחִ֑יו
Why does the Torah even need to added these words? Obviously if the "palit" told Avraham what happened, he heard the story, so why mention וַיִּשְׁמַ֣ע?
Because Avraham heard much more than he was told. He didn't hear, "My fellow countryman is in danger." He didn't hear, "My long lost nephew is in danger." What Avraham heard is, "My BROTHER is in danger."
That's a whole different attitude. That's what it means to have achvah.
כִּֽי־אֲנָשִׁ֥ים אַחִ֖ים אֲנָֽחְנוּ can be a tremendous thing, can motivate one in a positive way, but a person has to know where and when to give others some distance, so that אַל־נָ֨א תְהִ֤י מְרִיבָה֙