The support/query (S/Q) episodic training strategy has been widely used in modern meta-learning algorithms and is believed to improve their generalization ability to test environments. This paper conducts a theoretical investigation of this training strategy on generalization. From a stability perspective, we analyze the generalization error bound of generic meta-learning algorithms trained with such strategy. We show that the S/Q episodic training strategy naturally leads to a counterintuitive generalization bound of O(1/√n), which only depends on the task number n but independent of the inner-task sample size m. Under the common assumption m << n for few-shot learning, the bound of O(1/√n) implies strong generalization guarantees for modern meta-learning algorithms in the few-shot regime. To further explore the influence of training strategies on generalization, we propose a leave-one-out (LOO) training strategy for meta-learning and compare it with S/Q training. Experiments on standard few-shot regression and classification tasks with popular meta-learning algorithms validate our analysis.