Clinically acquired brain MRIs and radiology reports are valuable but underutilized resources due to the challenges of manual analysis and data heterogeneity. We developed fine-tuned language models (LMs) to classify brain MRI reports as normal (reports with limited pathology) or abnormal, fine-tuning BERT, BioBERT, ClinicalBERT, and RadBERT on 44,661 reports. We also explored the reasoning capabilities of a leading LM, Gemini 1.5-Pro, for normal report categorization. Automated image processing and modeling generated brain growth charts from LM-classified normal scans, comparing them to human-derived charts. Fine-tuned LMs achieved high classification performance (F1-Score >97%), with unbalanced training mitigating class imbalance. Performance was robust on out-of-distribution data, with full text outperforming summary (impression) sections. Gemini 1.5-Pro showed a promising categorization performance, especially with clinical inference. LM-derived brain growth charts were nearly identical to human-annotated charts (r = 0.99, p < 2.2e-16). Our LMs offer scalable analysis of radiology reports, enabling automated classification of brain MRIs in large datasets. One application is automated generation of brain growth charts for benchmarking quantitative image features. Further research is needed to address data heterogeneity and optimize LM reasoning.