Opinion summarization provides an important solution for summarizing opinions expressed among a large number of reviews. However, generating aspect-specific and general summaries is challenging due to the lack of annotated data. In this work, we propose two simple yet effective unsupervised approaches to generate both aspect-specific and general opinion summaries by training on synthetic datasets constructed with aspect-related review contents. Our first approach, Seed Words Based Leave-One-Out (SW-LOO), identifies aspect-related portions of reviews simply by exact-matching aspect seed words and outperforms existing methods by 3.4 ROUGE-L points on SPACE and 0.5 ROUGE-1 point on OPOSUM+ for aspect-specific opinion summarization. Our second approach, Natural Language Inference Based Leave-One-Out (NLI-LOO) identifies aspect-related sentences utilizing an NLI model in a more general setting without using seed words and outperforms existing approaches by 1.2 ROUGE-L points on SPACE for aspect-specific opinion summarization and remains competitive on other metrics.