Why is only one primer used for DNA sequencing instead of two?
The reaction for the Sanger sequencing reacting contains beneath the normal dNTP (which are needed to make most of the DNA) the dideoxynucleotides, which lack the 3'-OH-Group and which are labelled with a fluorescent dye. Once one of this nucleotides is incorporated, the chain reaction stops here, leading to a product with a specific length and a known (by the fluorescent dye) end base.

In theory this leads to products of a length primer + 1 ddNTP base, primer + 1 base + 1 ddNTP base, primer + 2 bases + 1 ddNTP base and so on. The sequencer seperates these bases by sizes and the sequentially reads out the fluorescent dye and translates this into a sequence of bases. See the image from the Wikipedia for illustration:



If you now add two primers (and of course have a double stranded DNA), this reaction will start from both ends of the DNA (always in 5'--> 3' direction) leading to two sets of marked DNA of the same size (so again the base + 1 ddNTP, base + 1 base + 1 ddNTP and so on). Since these are equal in size, you will always read out two bases at the same time and you will not be able to tell, which signal belongs to which strand. This looks like this (from here):