Mobile edge computing (MEC) has been considered to provide computation services near the edge of mobile networks, while the unmanned aerial vehicle (UAV) is becoming an important integrated component to extend service coverage. In this paper, we consider a UAV-enabled MEC with binary computation offloading, where a UAV serves as an aerial edge server and each task of devices is either executing locally or offloading to the aerial edge server as a whole. To provide fairness among different ground devices, we aim to maximize the minimum computation throughput for all devices via the joint design of computing mode selection and UAV trajectory as well as resource allocation. The optimization problem is formulated as a mixed-integer nonlinear problem consisting of binary variables, which is difficult to tackle. The influence of non-binary solutions is penalized with a penalty function, based on which we develop an efficient iteration algorithm to obtain a suboptimal solution via leveraging the penalty successive convex approximation (P-SCA) method and difference of two convex (D.C.) optimization framework, where the algorithm is guaranteed to converge. Extensive simulations are conducted and the results with different system parameters show the effectiveness of the proposed joint design algorithm compared with other benchmark schemes.