Because in the scriptures Jesus says that He and Heavenly Father are "one", people take that very literally and say, OK they are the same. Well the concept of the "Trinity" is not one found in the New Testament, but rather it is a man formed view of God. Harper’s Bible Dictionary records that “the formal doctrine of the Trinity as it was defined by the great church councils of the fourth and fifth centuries is not to be found in the [New Testament].” (Paul F. Achtemeier, ed. (1985), 1099)
Anyways, I was thinking about all the different situations that are recorded in the New Testament when Jesus is speaking to Heavenly Father and how weird it would be to think that He was actually talking to Himself... I mean, when He was hanging on the cross he asked Heavenly Father for the forgiveness of those who were crucifying Him. And then later when he is still there, He cries out "Eli, Eli, lama sabachthani? that is to say, My God, my God, why hast thou forsaken me?"(Matthew 27:46)
It just doesn't make sense to me (Heavenly Father and Jesus being the same person). And then I thought about Gollum in the Lord of the Rings talking to himself.. I know that drawing that parallel is boarder line blasphemous, but that is how I see it. God our Heavenly Father is one with Jesus Christ in every sense of the word, other than the same physical body. As Elder Jeffery R Holland stated in his October 2007 General Conference talk, "We declare it is self-evident from the scriptures that the Father, the Son, and the Holy Ghost are separate persons, three divine beings."
Some of the evidences I gave earlier show this point, also during Christ's prayer for His Apostles after the last supper. As recorded in St John chapter 17 (http://lds.org/scriptures/nt/john/17?lang=eng) "18 As thou hast asent me into the world, even so have I also sent them into the world.
19And for their sakes I asanctify myself, that they also might be sanctified through the truth.
21That they all may be aone; as thou, bFather, art in me, and I in thee, that they also may be cone in us: that the world may believe that thou hast sent me.
22And the glory which thou gavest me I have given them; that they may be aone, even as we are bone:"
If you'll read the whole chapter, it will give you a clearer understanding of the whole verses I just shared. Heavenly Father and Jesus Christ are two distinct individuals who have their own separate bodies. Another testament to this point is Joseph Smith's first vision in the Sacred Grove where he saw God the Father and Jesus Christ. I know the scriptures are true and that they are further proof that The Church of Jesus Christ of Latter-day Saints is the Lord's kingdom established once again onto the earth preparatory to the second coming of the Messiah!
Once again, if what I said doesn't make complete sense to you and you think I'm wrong, read this and it will explain it much better than I can http://lds.org/general-conference/2007/10/the-only-true-god-and-jesus-christ-whom-he-hath-sent?lang=eng&query=holland+whom+thou+hast+sent