A ray is a part of a line that has one end point but extends indefinitely in the other direction. Two opposite rays have a common endpoint and form a straight line.
Opposite rays need to meet at a point and have slopes with opposite signs. Just the fact that two rays have the same endpoint does not mean that they form a straight line. Any number of rays with different slopes can start at the same point. For any particular ray, there exists only one other ray that meets it at that point and the two are opposite rays.
All pairs of rays that have the same endpoint are not opposite rays as for each ray there is only one ray that forms a straight line.