The idea behind "chasing beta" is that high beta stocks have higher expected returns than low beta stocks. Therefore, if you are chasing absolute returns, then high beta is the way to go.
The idea does have a few flaws. First it assumes that there is a direct relation between historic beta and future returns. While academic studies have shown this to be true, the magnitude of the relation is below what theory predicts. Second, assuming that you can juice up your portfolio returns with higher beta, also assumes that your benchmark is not risk adjusted. A risk adjusted performance measure (such as alpha etc) would strip away this higher beta effect. Finally, why not just buy the low beta stocks (which by implication are being ignored) and then lever up?