How does a big ego and small ego exist in the same person at the same time? It sounds like a square triangle.
personally i think, the person who can't change his/her mind in light of new facts (which is what seems to be emphasized here) is dangerous.
i have _heard_ / _read_ that steve-jobs was known for changing his mind instantly in the light of new facts.
not sure, why this would be misconstrued as _weak_
Whether that's weak, I can't say.
Most people are one or the other (or somewhere in between) but to combine both in one human personality is quite rare. This may be a reason why people find it hard to work around and for such people.
Which is to say, be flexible, in your understanding, but resolute in your current belief.