The Bellman-Ford algorithm does not prevent routing loops from happening and suffers from the count-to-infinity problem. The core of the count-to-infinity problem is that if A tells B that it has a path somewhere, there is no way for B to know if the path has B as a part of it. To see the problem clearly, imagine a subnet connected like A-B-C-D-E-F, and let the metric between the routers be "number of jumps". Now suppose that A goes down (out of order). In the vector-update-process B notices that its once very short route of 1 to A is down - B does not receive the vector update from A. The problem is, B also gets an update from C, and C is still not aware of the fact that A is down - so it tells B that A is only two jumps from it, which is false. This slowly propagates through the network until it reaches infinity (in which case the algorithm corrects itself, due to the "Relax property" of Bellman Ford).
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