In this study, we present a new Deep Learning (DL) architecture for Motor Imagery (MI) based Brain Computer Interfaces (BCIs) called EEGSym. Our implementation aims to improve previous state-of-the-art performances on MI classification by overcoming inter-subject variability and reducing BCI inefficiency, which has been estimated to affect 10-50% of the population. This convolutional neural network includes the use of inception modules, residual connections and a design that introduces the symmetry of the brain through the mid-sagittal plane into the network architecture. It is complemented with a data augmentation technique that improves the generalization of the model and with the use of transfer learning across different datasets. We compare EEGSym's performance on inter-subject MI classification with ShallowConvNet, Deep-ConvNet, EEGNet and EEG-Inception. This comparison is performed on 5 publicly available datasets that include left or right hand motor imagery of 280 subjects. This population is the largest that has been evaluated in similar studies to date. EEGSym significantly outperforms the baseline models reaching accuracies of 88.6±9.0 on Physionet, 83.3±9.3 on OpenBMI, 85.1±9.5 on Kaya2018, 87.4±8.0 on Meng2019 and 90.2±6.5 on Stieger2021. At the same time, it allows 95.7% of the tested population (268 out of 280 users) to reach BCI control (≥70% accuracy). Furthermore, these results are achieved using only 16 electrodes of the more than 60 available on some datasets. Our implementation of EEGSym, which includes new advances for EEG processing with DL, outperforms previous state-of-the-art approaches on inter-subject MI classification.