Recent direct measurements of the growth kinetics of individual carbon nanotubes revealed abrupt changes in the growth rate of nanotubes maintaining the same crystal structure. These stochastic switches call into question the possibility of chirality selection based on growth kinetics. Here, we show that a similar average ratio between fast and slow rates of around 1.7 is observed largely independent of the catalyst and growth conditions. A simple model, supported by computer simulations, shows that these switches are caused by tilts of the growing nanotube edge between two main orientations, close-armchair or close-zigzag, inducing different growth mechanisms. The rate ratio of around 1.7 then simply results from an averaging of the number of growth sites and edge configurations in each orientation. Beyond providing new insights on nanotube growth based on classical crystal growth theory, these results point to ways to control the dynamics of nanotube edges, a key requirement for stabilizing growth kinetics and producing arrays of long structurally-selected nanotubes.