Breast Cancer (BC) has become a critical illness with a high mortality rate during the previous decade. It is considered the women’s most common cancer. In this paper, we propose two optimum automated BC classification approaches based on a hybridization of the Whale Optimization Algorithm (WOA) and Dragonfly Algorithm (DA), with Radial Basis Function Kernel Support Vector Machines (RBF-SVM), to increase the accuracy of BC classification (CA) by determining the optimum SVM parameters. The effectiveness of the proposed WOA-SVM and DA-SVM algorithms is tested on the Wisconsin Diagnosis Breast Cancer (WDBC) databases and the Wisconsin Breast Cancer Database (WBCD). Various metric parameters such as CA, confusion matrix, the area under the ROC curve (AUC), sensitivity, and specificity are utilized to assess and consider the effectiveness of the proposed approaches. The results are compared not only to the most common optimizers, Particle Swarm Optimization (PSO) and Genetic Algorithm (GA), that are used for training SVM and artificial neural networks (ANN) classifiers, but also to other classification models. The WOA-SVM and DA-SVM are also explored for feature selection, and their findings are compared to the offered models. According to the experimental results, the proposed WOA-SVM method outperforms previous classification approaches on the WBCD dataset. On the WDBC dataset, however, the proposed DA-SVM algorithm outperforms the previous classification algorithms. Using typical datasets’ partition, the resultant CA is as high as 99.65% and 100% for WDBC and WBCD, respectively. However, using a 10-fold cross-validation datasets’ partition, the mean resultant CA are 97.89% and 99.27%, respectively.