I tracked down this quote, and the actual quote is: '"There is a great man who makes every man feel small. But the real great man is the man who makes every man feel great.”'
This quote clearly differentiates between a man who makes it his M.O. to belittle everyone to feel superior himself, for example - Diamond Tiara... and someone who makes it his M.O. to make everyone feel better about themselves. They key here is the M.O.
The quote that OP posted does not provide this context, and so it is subject to misinterpretation.
The first way in which it could be misinterpreted is that in the absence of the more formal context, one could imagine it being written by an inferior man who just wants everyone to treat him well - the word "great," in this context, being subject to multiple interpretations... whereas in the original quote, it was clear that "great" referred to the traditional meaning. And so one might read the quote and assume that the person writing it just wants something for himself, which is the opposite of its original meaning.
The second way it could be misinterpreted is that the second part of OP's quote uses the word "everyone" instead of "every man" as in the original quote. This is a subtle but important difference, as a "man" is an individual with a set of individual principles and values, whereas "everyone" could be construed as merely the huddled, directionless masses that Plato once imagined as being only a notch more capable than authoritarians.
And so, for a superior man to try and make these huddled masses merely feel great and not actually become great, this would be a degradation of the really great man's character, in that he is reduced to prioritizing feelings and ignoring teaching the virtues and principles which give rise to healthy feelings to begin with.
As the original quote uses the terminology "every man," however, it is implies that in the process of the great man making others feel great, he appeals to the most human part of man - his logic, reason, and virtue... and so, to say that the great man makes every other man feel great, is to imply that he is in fact prioritizing their virtue and principles over their feelings, as good virtue and principles imply good feelings.