If water baptism is so important, why does the Bible not reference Jesus having water-baptized the twelve apostles?

If before the Baptism of the Holy Spirit, water baptism was so prevalent and important, why did Jesus not appear to have first of all water-baptized His twelve apostles but then sent them out to water-baptize others?

Indeed, Jesus Himself set the example of being water-baptized by John.  He subsequently arranged with His apostles/disciples to water-baptize others (John 4:2). Before Ascension, Jesus also commissioned the apostles to water-baptize others (Matt 28:19). 

If the apostles had not themselves been water-baptized, it appears strange that they went about water-baptizing others. 

The question comes about because in our bible study last night, we discussed the significance of water baptism in that apart from it being an outward declaration of our belief in God, Jesus’ own example signified His Trinity status and the beginning of Jesus’ three-year work.  Baptism also signifies the unity of all in Christ Jesus (Gal 3 :27-28 : for Jews, Greeks, bonded, free, male , female alike).  

Clarify • Share • Report • Asked March 19 2015 • Philip Wong