Adaptive streaming over HTTP/2 has recently caught attention in the development of multimedia delivery. The server push feature of HTTP/2 enables the streaming server to send multiple video segments to the clients within a single request, therefore reducing unnecessary overheads, RTTs and energy consumption on portable devices, also empowering the use of short segment duration to improve network adaptability. However, recent researches only investigate the performance of the HTTP/2 server push under a single-client scenario. In fact, when multiple clients share a limited bottleneck bandwidth, it is highly possible that the unfairness in bitrate selection will happen due to the mismatch of the segment download state among the clients. In this paper, we hypothetically discuss various cases that a client decides its bitrate higher or lower than one another. Then, an experiment with the DASH.js player under several scenarios is provided to confirm the reliability of our hypothesis.