Why does Pinchas who is Eliyahu Hanavi (Elijah the Prophet) come to Brissim and what does it have to do with this Parshas Pinchas?
The Bnei Yissochar answers it says in Parshas Pinchas:
תחת אשר קנא לאלוהיו ויכפר על בני ישראל
In Pirkie D'rav Eliezer it says:
Hashem saw Pinchas and asked him "What are you doing?" he answered and said he was angry for Hashem and Hashem told him you are always angry for Hashem in Shitim about the Immorality and here on the fact that they wait until you see the Bris with your own eyes.From Here we Have the Minhag to put a Chair for Eliyahu at every Bris as he is called the Angel of Circumcision.
The Bnei Yissochar said he heard of a Medrash on this where Eliyahu continues and tells Hashem what will be if I will be at the Bris of a sinner I wont be able to withstand him. Hashem answered and said I will forgive him.He went further and said what if the guests are sinners Hashem replied I will forgive them also,He went further and said maybe the Mohel will be a sinner Hashem answered I will forgive him too.
Now we can explain the Possuk: "תחת אשר קינא לאלוקיו"-Because you are zealous for Hashem. "קנאי לה'"-Therfore you can not stand sinners "ויכפר על בני ישראל" –Therfore all of the Jews will be forgiven.
Therefore he comes to Brissim to bear witness to Hashem's promise to grant everyone forgiveness, and the posuk in Parshas Pinchas explains why Hashem grants us this forgivness.