Because the Others Aren't Specific
Minister, it is a distinguished word isn't it? It conjures up thoughts of a man working with and for the congregation to fulfill the will of God through his constant encouragement and edification of the brethren. It fits! If you have spent even a day in the shoes of your local preacher you know that this is a perfect description of what he does. The day is filled with phone calls, hospital visits, errands and most likely picking up members of the congregation or the community for worship or Bible study. However, there's something that just doesn't fit. You see, the term is used in a number of different times in the New Testament (Acts 13:5, 24:23, 26:16, Romans 13:4, 15:8, 15:16, 15:25, 15:27, 1 Corinthians 9:13, 2 Corinthians 9:10, Galatians 2:17, Ephesians 3:7, 4:29, 6:21, Colossians 1:7, 1:23, 1:25, 4:7, 1 Thessalonians 3:2, 1 Timothy 1:4, 4:6, Hebrews 1:14, 6:10, 8:2, 1 Peter 1:12, 4:10, 4:11) and all of them speak to different rolls and people, not specifically speaking of the man employed by the congregation. Why? Because every Christian is to be a minister. If one were to read all of the above mentioned verses, he would quickly realize that there isn't a single thing mentioned therein that isn't the responsibility of any Christian regardless of the means by which he provides for his family.
Evangelist, a word which brings to mind a man working tirelessly to convert those in need and educate those that have obeyed. Men like Philip, the man responsible for speaking to the Ethiopian and baptizing him (Acts 8, 21:8), and Timothy (2 Timothy 4:5) are spoken of in this light. Yet, is that the role of the man of which we have been discussing? Yes and No. In my opinion, it would be detrimental for a man to be called the "worship leader" when other men were capable of leading in the congregational, corporate worship of the assembly on Sundays because it would detract from the responsibility of those other men to take upon themselves leadership roles from time to time within that same worship service. The same can be said of a man being called the "evangelist" when 1) every Christian is commanded to labor for the salvation of the lost (Mark 16:15-16) and 2) every Christian, regardless of whether or not we feel it is the case, is able to do just that!
Because "Preacher" Might Fit Better
I know the term doesn't carry with it the respect as some other terms, but isn't that what his role is? He is responsible for a large portion of the preaching of the Word of God to the congregation on Sundays during worship and the education of the congregation and community. While it is commanded of every Christian to "preach" (Mark 16:15), that is not to be done by every Christian during the worship times (cf. 1 Timothy 2:11). But what of the evangelism and ministerial work done by this man, it that of no account? Absolutely not! But aren't those things to be understood as the work of every Christian and not of one man per congregation? The difference is that the man under consideration has devoted his life to doing those things and is therefore compensated for his work for the church (1 Corinthians 9:14).
Now, I understand that the majority of this article has been opinion and that we ought not take this dogmatically, making laws where the Bible does not. However, these are simply some of this writer's rationale as to why I chose to, if allowed the opportunity to specify, be called a preacher rather than a minister or an evangelist. Plus, I grew a small town in Alabama, and those others just sound too sophisticated for a rough around the edges man like myself.