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It's known that when Avraham found out that Hashem was going to destroy Sodom and the other cities, he fervently argued with Hashem to save them.

My question is: when Hashem told Avraham to sacrifice his own son, why didn't Avraham at least try to argue in his defense, that he should be spared?

Ralbag has an interesting explanation of the challenge of the Binding of Isaac, which could answer this question.

He explains that the challenge was specifically to see how easy it would be for Abraham to sacrifice his son (i.e. not to see if he would sacrifice his son at all). God's command to Abraham was sufficiently vague that Abraham could have sought an interpretation other than "slaughter your son". The greatness of Abraham, according to Ralbag, was that he loved God so much that he did not seek to find an alternate understanding of the command. This is because when contrasted with his love of God, anything else — including his love for his son — is essentially non-existent. Thus, the test was to see whether Abraham's love of God was great enough that it totally overrode all other concerns, such that he did not even care to try to find an interpretation that would allow him to keep his son alive.

Accordingly, it is possible that Abraham didn't argue with God to spare Isaac for the same reason. That is, despite his love for Isaac his love for God was so great that killing his own son didn't even register as something he would want to avoid. There was thus no reason for him to beg god to spare Isaac.

When it came to Sodom, however, God had not commanded Abraham to do anything. Whereas trying to spare Isaac would necessarily have reflected an imperfection in Abraham's love of God, trying to spare Sodom would not have because regardless of Sodom being destroyed or spared Abraham would not be taking any actions for the sake of God. Therefore, Abraham could perfectly well request Sodom to be spared.

ולפי שהמובן ראשונה מזה המאמר הוא שיעלה יצחק שם לעולה בשיזבחהו ושישרפהו
הנה נשלם לה' יתעלה נסיון אברהם בזאת הנבואה אם יקל בעיניו לעשות איזה
דבר שיזדמן לכבוד ה' יתעלה וזה שאם יקל זה בעיניו לא יחזור להבין מזה
המאמר זולת מה שיובן ממנה בתחילת העיון ואם יקשה זה בעיניו יבקש לזה
המאמר כוונה אחרת זולת מה שיובן ממנו בתחילת העיון והנה הבין אברהם זאת
הנבואה לפי מה שיובן ממנו בתחילת העיון ועם כל זה נזדרז בחריצות גדול
לעשות מה שצוה לפי מחשבתו

התועלת הראשון הוא בדעות והוא להודיע לנו שאהבת ה' יתעלה יותר חשוקה
לשלימי הדעות מכל הטובות הנשארות עד שכבר יבוזו מפני האהבה ההיא בכל שאר
הטובות הלא תראה שאברהם השלם היה קל בעיניו לזבוח בנו יחידו אשר נולד לו
לעת זקנתו לכבוד ה' ולמלאת מצותו עד שלא התעורר לבקש כוונה אחרת למאמר
ה' יתעלה שיעלה יצחק בנו על ההר ההוא לעולה זולת מה שיובן מזה המאמר
בתחילת העיון

This exact question was also asked on Chabad.org and you can see their answer here.

Short answer that I heard from two rabbanim in my neighborhood:

Child sacrifice was considered the norm during that era. So, when G-d asked Abraham to sacrifice Isaac, he didn't think this was so unusual.

This is the explanation of Breishit 26:12 when G-d says, "Now I know that you are G-d fearing". You mean G-d didn't know this all along? (G-d knows everything!)

What is taught is that now everyone in the world will know that because you feared G-d and didn't sacrifice your son because I told you not to and you followed directions because you fear G-d, you are proof that child sacrifice is not "the Jewish way", unlike what the other nations do. And, the reason Jews in the future won't do it is because they will follow your example because you feared G-d.

I notice that the rabbis' explanation is a more specific expansion of what Rash"i says on this verse. So, they're explanation isn't theoretical.

I havent got a source for this (although I think I once heard something on these lines.)

There was no reason for Hashem to tell Avrohom about what he was planning to do to Sodom, so Avrohom deduced that Hashem wanted him to daven on their behalf.

With Yitzchok, this was a direct command from Hashem which made perfect sense why Hashem was telling him this, and Avrohom had no reason to suspect that God would be willing to back down on his command.