CNNs are the standard architecture for image classification because their convolutional layers exploit the spatial locality and translation invariance inherent to image data: learned filters detect local patterns (edges, textures, shapes) that compose hierarchically into higher-level features (parts, objects) as depth increases, without requiring the manual feature engineering that traditional models would need to reach comparable accuracy on raw pixel data. Pooling layers further provide a degree of spatial invariance, and parameter sharing across the image keeps the model tractable relative to a fully connected network operating on raw pixels.

Logistic Regression (A) is a linear classifier that operates on flattened feature vectors; applied directly to raw pixels of a 3-class image problem, it cannot capture the non-linear spatial structure needed to separate cats, dogs, and birds reliably, though it could serve as a baseline or as the final classification head atop CNN-extracted features. K-Means (B) is an unsupervised clustering algorithm — inappropriate here because the task is supervised classification with labeled classes. Linear Regression (C) predicts continuous outputs and is not designed for categorical class prediction at all.

For 10,000 labeled images, a CNN (potentially fine-tuned from a pretrained backbone via transfer learning, given the modest dataset size) is the appropriate and industry-standard choice.