How to go from technical to emotional
 

In my several dealings with my subordinates I find that when we do not agree on a point, I try to convince them logically what the problem and most often I win the logical argument but lose the empotional battle, i.e. the employee ends up feeling not so good.

As a manager, I find it more and more important for me to become less technical/logical and more empathetic, rather than winning the argument, I need to win the employee.

I would appreciate advice on what sort of steps I can take to move towards this direction?

Winning someone in a way that let's him feel good isn't about fighting battle's with them.
It's not about seeing them as enemy. It's about having friendly relationships with them.

Laugh more.

Don't treat them as if you get to decide what wins them over. They are people, not pawns, so you need their cooperation if you want them to like you. The quickest way to push someone away is to act as if you alone decide whether they get along with you, because it demeans their responsibility as humans. Treat their friendship and respect as something they can give you at their choice, instead of something you can be take from them if you act in a certain way.

Hi, Thanks for the responses so far. However, based on my original post you will notice I already realise what my problem is, what I am looking for is advice on things I could do during that moment (when tempers are high) to avoid such issues. When we are not arguing I usually share very good relationships with my employees and this post is an attempt to further strengthen those relationships.

You'll have to stop arguing, then. Arguments feed tempers, always. It's an extension of what I said before; just as you can't make your employees like you without their consent, you can't make them agree with you, even if you're right. An argument is an attempt to force something into being that isn't, such as understanding in an employee.

It's ineffective, because it doesn't acknowledge your limitations, and the power that your employee has to accept or deny your words. People tend to respond to force with force, regardless of the meaning behind the force. When you fight your employees, they will fight back. If you want your employees to make the right choices, you first have to show them that you want them to make choices. Only giving them space to make the decisions that you want them to make is no choice at all. Their ability to choose right is meaningless if they have no room to do it wrong.