Extracting accurate foreground animals from natural animal images benefits many downstream applications such as film production and augmented reality. However, the various appearance and furry characteristics of animals challenge existing matting methods, which usually require extra user inputs such as trimap or scribbles. To resolve these problems, we study the distinct roles of semantics and details for image matting and decompose the task into two parallel sub-tasks: high-level semantic segmentation and low-level details matting. Specifically, we propose a novel Glance and Focus Matting network (GFM), which employs a shared encoder and two separate decoders to learn both tasks in a collaborative manner for end-to-end animal image matting. Besides, we establish a novel Animal Matting dataset (AM-2k) containing 2,000 high-resolution natural animal images from 20 categories along with manually labeled alpha mattes. Furthermore, we investigate the domain gap issue between composite images and natural images systematically by conducting comprehensive analyses of various discrepancies between foreground and background images. We find that a carefully designed composition route RSSN that aims to reduce the discrepancies can lead to a better model with remarkable generalization ability. Comprehensive empirical studies on AM-2k demonstrate that GFM outperforms state-of-the-art methods and effectively reduces the generalization error.