Despite decades of research, discovering causal relationships from purely observational neuroimaging data such as fMRI remains a challenge. Popular algorithms such as Multivariate Granger Causality (MVGC) and Dynamic Causal Modeling (DCM) fall short in handling complex aspects of data such as contemporaneous effects and latent common causes. Decades of research on causal structure learning have developed alternative algorithms that address these limitations, but they often scale poorly with the number of variables and rely heavily on the lack of cycles in the underlying graph. Further, how existing algorithms compare in terms of accuracy and scalability when applied to fMRI has remained unknown. In this work, we first provide a detailed analysis of existing methods, finding Runge et al's PCMCI algorithm [1] and MVGC most accurate over simulated fMRI. However, neither algorithm is able to detect directed contemporaneous effects, a capability that is particularly important for fMRI. To address this gap, we propose the Causal discovery for Large-scale Low-resolution Time-series with Feedback (CaLLTiF) algorithm. This algorithm is based on PCMCI but improves upon it in terms of computational efficiency, cyclic contemporaneous connections, and statistical type I error control. CaLLTiF achieves significantly higher accuracy compared to existing algorithms in simulated fMRI. When applied to resting-state fMRI from human subjects (n = 200, Human Connectome Project), causal connectomes learned by CaLLTiF show higher sparsity and consistency across subjects than functional connectivity and align with known resting-state dynamics. These graphs also capture Euclidean distance-dependence in causal interactions, while demonstrating statistically significant laterality and gender differences. Overall, this work provides a clear picture of the critical gap between the capabilities of existing algorithms and the needs of causal discovery from whole-brain fMRI, and proposes a new algorithm with higher scalability and accuracy to address this gap. This study further paves the way and defines a standard for future investigations into causal discovery from neuroimaging data.