I'm having some difficulty understanding the incident of the Akaida. God tested Avraham by commanding him to take his son as a human sacrifice to see if he would obey even this (Genesis 22). However, I am confused by this. Isn't it considered objectively very bad to kill one's son, no matter how much they believe that God wants them to do that? It seems one should expect that objective morals always overrule what someone believes to be commands from God since it could be that they are wrong or mistaken, and in Avraham's case, shouldn't he have been tipped off the the possibility that God wouldn't want him to do that by virtue of the fact that it was a human sacrifice?
This is a really important question.
It seems one should expect that objective morals always overrule what someone believes to be commands from God since it could be that they are wrong or mistaken...
Your question is based on two premises. The first is that an ethic independent of God's will exists. As can be seen in the comments section, this is not a simple issue. The way you've phrased it also indicates that it's something you're not so sure of. Regardless of whether such a thing exists however, there is no question that the Torah itself sees murder as morally reprehensible so the question of how could Avraham attempt to carry out such an action is a valid one.
Your second premise is that Avraham could have been mistaken regarding what God commanded him. This is the the premise which fails. The Rambam writes in his Guide to the Perplexed (3:24) that the story of the Akeidah is a source which proves that when a prophet receives a message from God, he receives its content with absolute certainty. Had Avraham had any doubt whatsoever regarding whether this was God's intention, he would never have attempted to carry it out. Accordingly, Avraham was left between a hard place and a rock. On the one hand, he knew that murder was absolutely morally reprehensible. On the other hand, God had unequivocally told him to kill his son. In such a case it is God's direct command which must prevail and this is exactly the point. Man cannot understand God. He is supposed to try his hardest to do so but it is inevitable that the finite will fall short of the infinite. As such, Avraham didn't know why he was supposed to kill his son but he did know that God wouldn't have commanded it if it wasn't the right thing to do.
Perhaps this is best demonstrated with an example. Suppose you found yourself stuck as the only physically fit individual on an island. A surgeon tells you that you need to carry out an amputation on someone else. On the one hand, you know that hacking off people's limbs is wrong. On the other hand, someone moral and more knowledgable than you is telling you that you have to do so. You might not know why but you do know that following the command is the right thing to do. This was essentially Avraham's situation.
There are a lot of other questions regarding the Akeidah which still need to be dealt with but I think the above provides a coherent answer to the one you asked. Note also that this is just one approach to begin understanding the Akeidah and there are many others. A whole series of Shiurim going through different approaches can be found here.
you started by making the assumption that the only reason for the akeda was to test if Abraham would follow G-d's command but there is another underlying motive here which is a powerful way of conveying to us that children belong to G-d and not their parents. As such sacrificing them to fulfill religion is wrong. Gd demonstrated this by having Abraham go through with the process right up until before the killing was to take place. Rabbi Jonathan Sacks explains this idea more eloquently than I.