Why does it sound like it? She isn't identified as "the" servant of the church. Phoebe is identified as "a" servant in the church of Cenchrea. Phoebe is really sketchy ground imho. Too often egalitarians (I'm not saying you are one) try to reach into this verse and make it say stuff it doesn't say. The stronger case is Junia (which I doubt was an apostle.)
The language used here, the Greek, isn't unique or special. Paul says she is part of a church and serves that church. There isn't unique language used to denote an office. In light of 1 Timothy 3:12 I don't think it is an easy case at all.
I understand that but again you've got to show me in the NT where women served in the office of deacon. I don't think that is an easy case to make.
First, not sure I see a difference between being "the servant" and "a servant" as it relates to proving she was or was not a deacon. However, neither the word "the" or the word "a" was used by Paul, so it is a moot point.
As far as it being sketchy ground, it is only sketchy b/c you have a tradition that says no in light of the fact that she is given the same term that Paul uses in other places. You might have a point except that the term is related to ministry in the local church. That is big.
As for "unique language used to denote an office"... that doesn't exist for any church office. Pastor, elder, overseer, deacon... these were all common words interpreted in the NT as offices of the church. So in light of that, using a common term for a church office makes the situation grey.
As for showing you in the NT of a woman deacon, I'd ask you to do the same with men. Name 1 male deacon in the NT. BTW... Acts 6 doesn't say they were deacons, so that can only count if PHoebe can count (since the actual term was used for her and restricted to a local church!). Maybe I'm forgetting one or two, but none come to my mind. Of course, referring to 1 Tim 3 only works if you mention the fact that both male and females are mentioned there.
BTW... this should probably be a separate thread so as not to continue this hijack.