Boromir was a little ego-centric. I believe this passage shows his pride was hurt that the ruler of the greatest kingdom in M-E was not "king," and therefore, Boromir would not be "king."
If I recall, from the last "Alas! poor Boromir," quote from Faramir, he goes on to say that the temptation to take the Ring was too great for one such as Boromir who had ambition to grow in power.
I do not see Denethor instilling any bitterness in Boromir at least in this exchange. However, would not Boromir have sensed any bitterness or resentment in Denethor related to the King versus Steward role? I mean, if there were any present. If so, it would likely have been internalized by the son.
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For I was talking aloud to myself. A habit of the old: they choose the wisest person present to speak to; the long explanations needed by the young are wearying. -Gandalf, The Two Towers
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