Question:It seems that we do not follow the Rambam's opinion (Teshuva 2:5) to publicly announce our sins between man and his fellow. If my observation is correct, why is this?

Answer:The gemara (Yoma 76b) discusses the appropriateness of two related steps one might include in the teshuva (repentance) process. One is specifying the aveira (sin) he transgressed, which is the subject of a disagreement among Tannaim if it is necessary. A few lines earlier, the gemara raises an apparent contradiction between p’sukim: one says, "Praiseworthy is one who … covers up sin" (Tehillim 32:1); the other says, "One who covers up his sins will not succeed" (Mishlei 28:13). The gemara provides two distinctions to reconcile the p’sukim: 1. One admits publicized sins; one conceals unpublicized sins; 2. One publicizes sins between man and his fellow man; he keeps quiet about sins between man and Hashem. The Rambam you cited mentions only the second distinction, and speaks positively about publicizing sins to his fellow as part of the teshuva process.
The Shulchan Aruch (Orach Chayim 607:1) recommends but does not require specifying one’s sins. If one does not have to specify a sin, he obviously does not have to publicize it (publicizing refers to specific sins- see Bach, OC 607). Indeed the Shulchan Aruch does not mention publicizing sin as part of the process. All he says regarding involving others is that when one is appeasing someone he slighted, he takes three people with him up to three times if the victim does not forgive him at first (OC 606:1).
In truth, while the Rambam requires specifying sins (Teshuva 2:3), he does not require publicizing sins. Rather, in Teshuva 2:5 he says: "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." The previous halacha recommends the repenting sinner to "scream constantly before Hashem in tears … and go into exile …" The Rambam thus is apparently talking about some combination of the following situations: someone who decided to perform a very high level of teshuva; the perpetrated sin was particularly grievous. Otherwise the steps recommended are extreme. The language and context implies that publicizing is done in similar situations.
There are other factors that justify not publicizing sins toward one’s fellow man. Rashi (Yoma 86b) says that one publicizes because embarrassment helps in the atonement. However, embarrassment can also hold people back from action. We find, in certain monetary contexts, takanot hashavim: special dispensations made for those who sinned, for would they be held to the strict law, many would lack the moral commitment to repent (see Gittin 55a). Certainly when the letter of the law suffices with privately appeasing the victim, demanding the sinner to reach high levels of teshuva may be counterproductive for many.
Secondly, the embarrassment often affects the victim as well. Making a big deal of the affront may relive the event or focus the public’s attention on the victim’s weakness that was exposed during the sin. In Living the Halachic Process, vol. I, H-5, we explained that the sinner should not further hurt the victim as part of the teshuva process. The Mishna Berura (606:3) says that one should not specify the aveira while appeasing the victim if it will cause him pain. If that applies to specifying, which is a more integral part of the teshuva process, certainly it applies to publicizing.
Thus we can summarize our response to your observation that people do not publicize their sins toward others, as follows. The Rambam apparently only recommended it, for great people or severe affronts, both of which are rare (indeed, on rare occasions, there are public apologies). In any case, basic teshuva does not require it, explaining why the Shulchan Aruch does not mention it. Where the prospect of publicizing will either discourage repentance or cause the victim pain, it is counterproductive.