Raising daughters is tough for a dad. The reasons are probably quite obvious, but I will give a brief overview.
A father will almost always struggle to relate to his teenage girls. When he was growing up he was probably a brute. Didn't care much about how he looked, classic teenage boy. Now, suddenly he has a daughter who thinks that how she looks is what the entire world revolves under. Her passions suddenly change from wanting to spend time with daddy, to wanting to spend time at the mall. They care about eyebrow waxing and shaping more than they care about spending time with family.
Fortunately, that is part of life! We don't have to be able to relate to somebody to be able to have a good relationship with them. In fact, some of the best relationships on earth are actually built when two people do not relate to each other, but find a way to get around their differences. While watching politics today might make you think that getting along with different mindsets is impossible, it is actually quite possible (though not so much today in politics).
The best is to not necessarily try to understand your daughters. You may never be able to understand why they act the way they do. They are teenagers! Things are changing quick, both in life and hormonally. Sometimes they might not even make sense. If you spend all of your time trying to understand what makes them tick, you may have wasted a lot of time.
The real key os to focus on something that you will always be able to do. Love them. Who cares if they are confusing and perhaps have some issues that often come with growing up as a teenager in today's society. You can always love them and show them that you love them. If they can see that you love them, you will always be able to have a good relationship with them. Love transcends all.
The second key is to not always give in to them. Teenagers make some pretty bad decisions sometimes. Parents often feel pressured to give in to the teenagers because they feel that their relationship will be damaged if they stop their daughters (or sons) from doing something. However, your job as a parent is to make sure your kids don't get into life-altering trouble. You can let them make mistakes, but not mistakes that could change the course of their life.
This also comes down to step one. If your kids know that you love them, they will eventually be able to understand why you denied letting them do something that they really wanted to do. They will eventually appreciate that you cared enough to block them from ruining their life.
It will never be easy to be a parent. The third key is just to do your best!