What is the issue with Metzizah B'Peh? Why would some stop an age old minhag, even if there is a remote possibility of a health issue? why are there those who feel it is not allowed? And if I may ask what was the history regarding its practice until now?
Answer:
It isn't possible, in this forum, to give a complete answer. I will give a brief summary alone.
The Mishnah teaches that there is a need for metzitzah, and the Gemara explains that this is for medical purposes. For the sake of the infant's safety, it is permitted to perform metzitzah even on Shabbos, in spite of the fact that this constitutes a melachah.
However, it does not say anywhere that the metzitzah (suction) must be with the mohel's mouth. The Chasam Sofer was asked by the Rav of Vienna if under extenuating circumstances -- babies that were being infected with a dangerous disease because of oral suction -- suction can be performed by alternative means, and he answered that this is fine, noting that the kabbalistic reasons given for oral suction do not weight strongly enough for such circumstances.
Yet, the response was never published in the Teshuvos of the Chasam Sofer himself.
In the subsequent generation, the issue of oral suction became a heated arena for the fight between reformers and traditionalists. The doctor who informed the rabbi of Vienna became known as a reformer Jew who despised oral metztitzah as a "despicable" practice, and the ardently traditional Hungarian rabbinic community was up in arms. The "reformers," however, claimed that the practice was outdated, decadent, and dangerous, and that it should be replaced altogether.
Several responsa were written by such luminaries as the Maharam Schick and others explaining that there was no proven medical reason not to perform oral suction, and arguing that because it was the custom (and for other reasons) the practice gains weighty halachic status. Some even suggested that it becomes a "halachah le-Moshe mi-Sinai"!
Later, a new method of suction was invented, by means of a glass cylinder (which forms a vacuum by means of suction), and many communities adopted it, including communities in Germany and in Lithuania. Some actually refrained from suction on Shabbos altogether.
Today, most Charedi communities continue to perform oral suction in the traditional manner, whereas more modern communities use an alternative. This is in spite of a number of tragedies that occurred in recent years of babies becoming infected with herpes, some of them dying -- a state of affairs that has caused the practice to be frowned on by US health authorities.
It should be noted that a number of poskim, in particular those who come from Hungarian backgrounds, continue to write with great zeal concerning the obligation to perform oral suction (for instance: Shevet Ha-Levi; Minchas Yitzchak; and more than all others, Mishnah Halachos).
Nonetheless, poskim (Shevet Ha-Levi) write that concerning a bris performed for adults, one can use an alternative method of suction, the reason usually being given as protection for the mohel from potential diseases.
There is far more to write here, but a full article is really required.