Encourage One Another

I read through Hebrews the other day and was struck by the "one another" passages, especially the ones related to the encouragement of one another (Heb 3:13). I thought about how in my life I am actively seeking to encourage those around me, and then thought if my encouragement was done out of selfish ambition or vain conceit (Phil. 2:3).
Doing things for others can come naturally for some - a word of encouragement or a display of hospitality - but the end goal of the encouragement is significant. Is it simply to say or show that you have been encouraging or is it to encourage the person on towards Christ?
Some of this ties back to what one of my professors said while he had a group of students over for lunch. At the end of the time he said "I just ask that you open up your house as well." He was clearly not just blessing and encouraging us through the serving of food and opening of his house, but he was seeking to encourage us to be more Christ-like in our own hospitality and loving of one another.
The end goal of becoming more like Christ and encouraging others to be more like Christ should be at the forefront of our minds, actions and hearts especially as we seek to love and serve one another.