My dear friend, I beg you will not suppose that the admission you have so candidly offered must immediately condemn your character or place you beyond the reach of understanding. Many a person has found himself perplexed by the curious workings of his own sentiments, discovering within himself a certain coolness of feeling where he expected warmth, and wondering with no small concern what such a condition might signify. Yet the very fact that you experience guilt or unease at this absence of empathy speaks not of a heart wholly indifferent, but rather of a mind attentive enough to examine itself with honesty.
It would be unwise, I think, to rush toward any severe judgment of your nature upon so limited a reflection, for the dispositions of the human mind are often intricate, and what appears at first to be a settled trait may in time reveal itself to be but a passing confusion or an unexamined burden. Should these thoughts trouble you greatly, there would be no shame in seeking the counsel of one skilled in such matters, who might guide you with patience and clarity.
In the meantime, I would encourage you to treat yourself with the same measure of charity you would extend to another in distress. For self-understanding, like all worthwhile pursuits, proceeds not by harsh accusation but by quiet reflection and careful inquiry.