IMHO, it's a double-edged sword...

On the one hand, an apology is coming from a vulnerable place - it is admitting that the apologizer had an assumption about something that was inaccurate and realized it retroactively...

One of the unspoken social rules that is often (unconsciously) followed is the goal in looking good to one's fellow peers. When one realizes an error in discernment has taken place, and that an apology is necessary to set things right, it is taking the risk of not looking good by admitting that one was mistaken, and thus not coming from a place of true strength or clear intelligence...

On the other hand, an apology is coming from a place of strength - it is courageously risking not looking good to one's fellow peers and is openly admitting that one is human, capable of error, and even fallible at times...

Most people can admit this in general - but when one is admitting it personally... It takes honest conviction and an adherence to principles that, unfortunately, many people simply don't have. And this is why, IMHO, there is such a great amount of respect for people who are brave enough to risk not looking good - one is adhering to principles and being true to oneself. Essentially, one is refusing to give a flying fuck how one is perceived by others...

So while one is admitting error, one is also admitting strength - thus the double-edged sword. :-)