Existing text style transfer (TST) methods rely on style classifiers to disentangle the text's content and style attributes for text style transfer. While the style classifier plays a critical role in existing TST methods, there is no known investigation on its effect on the TST methods. In this paper, we conduct an empirical study on the limitations of the style classifiers used in existing TST methods. We demonstrated that the existing style classifiers cannot learn sentence syntax effectively and ultimately worsen existing TST models' performance. To address this issue, we propose a novel Syntax-Aware Controllable Generation (SACG) model, which includes a syntax-aware style classifier that ensures learned style latent representations effectively capture the sentence structure for TST. Through extensive experiments on two popular text style transfer tasks, we show that our proposed method significantly outperforms twelve state-of-the-art methods. Our case studies have also demonstrated SACG's ability to generate fluent target-style sentences that preserved the original content.