We present a qualitative analysis of the variability of quasar broad absorption lines using the large multi-epoch spectroscopic data set of the Sloan Digital Sky Survey Data Release 10. We confirm that variations of absorption lines are highly coordinated among different components of the same ion or the same absorption component of different ions for C IV, Si IV, and N V. Furthermore, we show that the equivalent widths (EWs) of the lines decrease or increase statistically when the continuum brightens or dims. This is further supported by the synchronized variations of emission and absorption-line EWs when the well-established intrinsic Baldwin effect for emission lines is taken into account. We find that the emergence of an absorption component is usually accompanied by the dimming of the continuum while the disappearance of an absorption-line component is accompanied by the brightening of the continuum. This suggests that the emergence or disappearance of a C IV absorption component is only the extreme case, when the ionic column density is very sensitive to continuum variations or the continuum variability the amplitude is larger. These results support the idea that absorption-line variability is driven mainly by changes in the gas ionization in response to continuum variations, that the line-absorbing gas is highly ionized, and in some extreme cases, too highly ionized to be detected in UV absorption lines. Due to uncertainties in the spectroscopic flux calibration, we cannot quantify the fraction of quasars with asynchronized continuum and absorption-line variations.