When aligning paired reads, alignment tools may assume that your R1 and R2 fastq files are sorted in the same order. When we provide R1 and R2 fastq files to you, they are sorted correctly.
However, if you preprocess your reads in a manner that changes the order of the reads, this can result in the wrong reads being treated as pairs. In this case, the aligner reports a high percentage of discordant alignments.
Alternatively, if your read length is small and adapter trimming has been performed, it is possible that some reads have been entirely trimmed and have 0 length. This will result in a blank read in your fastq file. Some tools such as TopHat will skip such reads, resulting in all subsequent read pairings being mismatched. To resolve this issue, you can preprocess your reads with Trimmomatic and specify a minimum read length.