The gemara[2] discusses the appropriateness of two related steps a person might include in the teshuva[3] process. One question is whether he should specify the aveira[4] he transgressed, which is the subject of a disagreement among Tannaim. The other question is whether one should publicize the sin. Regarding the second question, the gemara raises an apparent contradiction between p’sukim. One pasuk says, “Praiseworthy is one who … covers up sin”[5]; the other states, “One who covers up his sins will not succeed.”[6] The gemara provides two distinctions to reconcile the p’sukim: 1) One should publicly acknowledge publicized sins; he should conceal unpublicized sins. 2) One should publicize sins between man and his fellow man; he should keep quiet about sins between man and HaShem. The Rambam you cited mentions only the second distinction and speaks positively about publicizing sins one did to his fellow, as part of the teshuva process.
The Shulchan Aruch[7] recommends specifying one’s sins, especially quietly, but does not require doing so. If one does not have to specify a sin, he obviously does not have to publicize it (publicizing refers to specific sins[8]). Indeed, the Shulchan Aruch does not mention publicizing sins as part of the process. All he says about involving others is that if one is trying to appease someone he slighted, if the aggrieved party does not forgive him at first, he should take three people along with him up to three times.[9]
In truth, while the Rambam does require specifying sins,[10] he does not require publicizing them. Rather, he writes: “It is very praiseworthy for one who repents to admit the matter in public … and whoever is haughty and does not inform others but conceals his sins does not have complete teshuva.”[11] The previous halacha recommends the repenting sinner to “scream constantly before HaShem in tears … and go into exile ….” In order to warrant such extreme steps, the Rambam must be referring to one who perpetrated a particularly grievous sin and decided to perform a very high level of teshuva. My preferred reading of the Rambam is that the halacha about publicizing one’s sins is referring to similar situations. Accordingly, in the case of simple sins that most people perpetrate, we would not expect a public pronouncement of remorse and apology.
There are other factors that justify not publicizing sins toward one’s fellow man. Rashi[12] says that one publicizes his sin in order to be embarrassed. Apparently, the embarrassment makes him more likely to attain atonement. On the other hand, embarrassment can also restrain people from taking action. In certain monetary contexts we find the concept of takanot hashavim, special dispensations made for those who sinned. Were they to be held to the strict law, many would lack the moral commitment to repent.[13] Similarly, when the letter of the law requires only privately appeasing the aggrieved party, demanding the sinner to reach high levels of teshuva by publicizing his sin may be counterproductive.
Moreover, there is sometimes embarrassment not only for the sinner but for the aggrieved party as well. Making a big deal of the affront may cause the aggrieved party to painfully relive the event. Also, focusing the public’s attention on what took place may be detrimental to the aggrieved party in a variety of different ways. Elsewhere,[14] we explained that one who sinned against his counterpart should not hurt him further in order to facilitate the teshuva process. Indeed, the Mishna Berura[15] writes that one should not specify the aveira while appeasing the aggrieved party if it will cause him pain. If pain to the aggrieved party is sufficient reason for the sinner to omit specifying the sin, which is generally a required part of the teshuva process, certainly it is reason for him to omit publicizing it, which is only recommended.
In summary, the Rambam apparently only recommended publicizing sins for people seeking the highest level of teshuva and/or for severe affronts, both of which are not very common. (Indeed, on rare occasions, there are public apologies.) In any case, basic teshuva does not require publicizing one’s sins, which explains why the Shulchan Aruch does not mention it. In cases in which the prospect of publicizing will either discourage repentance or cause the aggrieved party pain, it is actually counterproductive.