The reason some people believe Eve was created on a later date is because they interpret Genesis 2 to be chronologically after Genesis 1. This is not what the author intends, as Genesis 2 is a retelling of the events in Genesis 1 with greater detail. Modern literature is almost always written in chronological order so this retelling can confuse people--but Genesis 2 is not a chapter of events following Genesis 1, but a retelling of it.
Genesis 2:5-7 ESV When no bush of the field was yet in the land and no small plant of the field had yet sprung up—for the Lord God had not caused it to rain on the land, and there was no man to work the ground, and a mist was going up from the land and was watering the whole face of the ground— then the Lord God formed the man of dust from the ground and breathed into his nostrils the breath of life, and the man became a living creature.
In verses 5-7 he's talking about the state of the world before he created man on day 6. Look at the verses immediately following these:
Genesis 2:8-9 ESV And the Lord God planted a garden in Eden, in the east, and there he put the man whom he had formed. And out of the ground the Lord God made to spring up every tree that is pleasant to the sight and good for food. The tree of life was in the midst of the garden, and the tree of the knowledge of good and evil.
[more detail about the rivers and gold and stuff]
Genesis 2:18 ESV Then the Lord God said, “It is not good that the man should be alone; I will make him a helper fit for him.”
Verses 10-18 talk about various rivers, gardens, and lands, and it's not until verse 18 that a helper suitable for Adam is mentioned. This, again, is just a retelling of chapter 1 with a different emphasis on detail. Those that don't realize it's a retelling but think it to be a compounding sequence of events may easily reach the conclusion that Eve was created long after Adam.
It is worth saying, however, that this viewpoint causes a contradiction with Genesis 1 which states that mankind, male and female, were made on Day 6.
Genesis 1:27,31 ESV So God created man in his own image, in the image of God he created him; male and female he created them ... And God saw everything that he had made, and behold, it was very good. And there was evening and there was morning, the sixth day.