The problem is simple: Mary Magdalene is presented in the synoptic gospels as having seen an angel or angels at the tomb, heard him or them announce the resurrection of Jesus, after which she actually encountered Jesus and worshiped him as she was running from the tomb to tell the disciples what had happened. In John's gospel, however, Mary Magdalene is presented as having found the tomb empty, after which she ran to Peter and the disciple "whom Jesus loved" and told them that the body had been stolen. So the problem is why Mary would have told the disciples that the body had been stolen if she had seen and heard everything that the synoptic gospels claim that she saw and heard.
In order to get to the heart of the problem much quicker, let me give a rebuttal of the most commonly used "explanation" for this problem.
Many inerrantists contend that Mary Magdalene simply panicked when she saw the empty tomb and ran to Peter before she had heard the angel(s) announce that Jesus had risen. This "explanation," however, is completely incompatible with Matthew's gospel account. Let's look at it first, and then I will explain why the explanation is incompatible with what "Matthew" clearly said.
I have emphasized in uppercase letters certain words to call attention to them. They will establish that Matthew intended for his readers to understand that Mary Magdalene didn't just hear the angel announce that Jesus had been raised from the dead but that she also saw him and touched him after she had run from the tomb. To establish this, let's notice that Mary Magdalene and the other Mary are the ONLY two women mentioned in Matthew's version. The fact that Mark and Luke may have mentioned other women has nothing to do with the obvious fact that Matthew mentioned only two women: Mary Magdalene and the other Mary. Therefore, "THE WOMEN" in verse 5 to whom the angel said that Jesus had risen must have necessarily included Mary Magdalene; otherwise, Matthew's text is incoherent and would not have conveyed an accurate picture of what had happened to early Christians who may have lived and died having had access only to this one gospel account. I assume that inerrantists are willing to admit that the NT in bound volumes didn't exist until many years after the gospels were written, so a reader of Matthew very likely would have been unable to consult Mark, Luke, and John to see if they shed any "additional light" on what had happened. If nothing else, Christians living at the time Matthew's gospel was completed could not have had access to Luke and John, since (as most biblical scholars agree) they were written after Matthew. Therefore, the picture they formed in their minds after reading Matthew's gospel could not have included anything that was written in gospels that came after Matthew's.
Besides this, there are linguistic factors that those defending the accuracy of the Bible must consider. All rules of literary interpretation that I ever heard of (and I studied a lot of literature on the subject during my 30 years teaching college English) would require readers to understand that "THE WOMEN" in verse 5 of Matthew's text were Mary Magdalene and the other Mary. No other assumptions can be made, since Matthew did not himself specify that any other women were with the two Marys. Furthermore, the rules of pronoun-antecedent agreement will require readers to understand that the antecedent of the pronouns "THEY" and "THEM" (emphasized in uppercase letters) is "THE WOMEN." Since "THE WOMEN" had to be Mary Magdalene and the other Mary, then the antecedents of "THEY" and "THEM" are indirectly (by necessity) Mary Magdalene and the other Mary.
It is a rule of literary interpretation that the substitution of antecedents for the pronouns in a text will not alter the meaning of the text but will, if anything, help clarify the meaning of the text. With that in mind, I will now take Matthew's text quoted above and present it with the antecedents substituted for the pronouns "THEY" and "THEM."
It is therefore evident that Matthew meant for his readers to understand that Mary Magdalene heard an angel announce that Jesus had risen AND that she ran from the tomb with great joy after hearing this AND that she met Jesus and touched him after she had run from the tomb.
So my question to those who defend the Bible as consistent and without error, is this: If Mary Magdalene had been told by an angel that Jesus had risen and if she had even seen Jesus and touched him after leaving the tomb, why did she go tell Peter that the body of Jesus had been stolen?
And another problem with the Mary Magdalene story:
According to Mark, upon witnessing the empty tomb, they went and told no one: And when the sabbath was past, Mary Magdalene, and Mary the mother of James, and Salome, had bought sweet spices, that they might come and anoint him. And very early in the morning the first day of the week, they came unto the sepulchre... And they went out quickly, and fled from the sepulchre: for they trembled and were amazed: neither said they any thing to any man; for they were afraid. Mark 16:1, 2, 8
According to other verses, upon witnessing the empty tomb, they went quickly and ran to tell all the disciples: And they departed quickly from the sepulchre with fear and great joy; and did run to bring his disciples word. Matt. 28:8 And they remembered his words, and returned from the sepulchre, and told all these things unto the eleven, and to all the rest. Luke 24:8 Then she runneth, and cometh to Simon Peter, and to the other disciple, whom Jesus loved, and saith unto them, They have taken away the Lord out of the sepulchre, and we know not where they have laid him. John 20:2 Yea, and certain women also of our company made us astonished, which were early at the sepulchre; And when they found not his body, they came, saying, that they had also seen a vision of angels, which said that he was alive. And certain of them which were with us went to the sepulchre, and found it even so as the women had said...: Luke 24:22-24.