There's already good answers here, so I'll add in what I think are some of my techniques for constructing rounded characters.
Making Strengths Into Weaknesses
Ever heard the phrase 'honest-to-a-fault'? Even the most noble and virtuous of attributes can become weaknesses if they are improperly moderated.
It's easy to stretch a trait such as determination and turn it into ruthlessness, having someone so single minded on achieving a goal that they will climb over others in order to get there. People who have a great work ethic can sometimes also be stubborn when it comes to admitting defeat.
In your example, having someone who is wise and experienced may also make them stubborn and close minded, unwilling to listen to the opinion of others because he believes that he is correct due to his greater levels of experience.
Making Them A Hypocrite
Nobody is perfect, and sometimes even the most idealist of people can fall off of the wagon.
Having someone following their own rules all the time to the letter doesn't always make the most interesting character. Interesting moments occur when a character has their ideals tested, and then they may break them for 'the greater good', or to help achieve their goals in the long run.
Characters don't have to be a "do as I say, not as I do" type of person, sometimes it's just impossible for people to maintain their views all of the time. They may be challenged in such a way as they will change their beliefs in order to fit with new revelations, going entirely against something that they staunchly maintained previously.
Your example character may train your hero for a long time, building them up to accomplish a certain goal/ quest, only at the last minute to sabotage their chances in order to allow room for the anti-hero to tackle the challenge instead, as he believes they are more experienced/ qualified to handle it despite the training that the hero has received.
That's a pretty radical example, but it can make a character more interesting to realize that they were only being kind in order to use the hero as a means to an end, and switching as soon as a better option presented itself.
Having Compatible Qualities
Similar to the "strengths into weaknesses" point, certain qualities fit with certain types of people, whereas others don't. As suggested in another answer, pride would work very well based on the description of your example character.
There are certain things that would be very incompatible, and would be a difficult character to make believable. For example having a character who is helpful and performs kind deeds for others anonymously, but they're also a narcissist, would be a struggle to pull off. Why would someone who is self-absorbed perform these acts in the first place, of they weren't doing it to receive recognition? Or a self-made business tycoon who is lazy; they wouldn't be able to achieve such success if they had that flaw.