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Here is an example of how to design a simple CNN architecture for image classification:

1. Start with a simple network: We'll start with a simple architecture and add complexity if necessary.

2. Determine the input and output layers: Since we're working with images, our input layer will be the image itself. We'll use 32x32 pixel images and normalize the pixel values between 0 and 1. Our output layer will have two nodes, one for cats and one for dogs.

3. Choose the number of hidden layers: For this problem, two or three hidden layers should be sufficient. We'll experiment with both to see which works better.

4. Determine the number of nodes in each layer: For the first hidden layer, we'll use 32 nodes. For the second hidden layer, we'll use 64 nodes. We can experiment with the number of nodes in the third hidden layer if we decide to add one.

5. Choose the activation function: For this example, we'll use the ReLU activation function for all hidden layers. For the output layer, we'll use the softmax activation function, which is commonly used in multi-class classification problems.

6. Choose the loss function: Since this is a multi-class classification problem, we'll use the categorical cross-entropy loss function.

7. Experiment with different architectures: We can experiment with different numbers of hidden layers, nodes in each layer, and activation functions to find the best architecture for our problem.

Here's what the overall architecture would look like:

```
Input layer (32x32x3)
Convolutional layer with 32 filters and 3x3 kernel size, ReLU activation
Max pooling layer with 2x2 pool size
Convolutional layer with 64 filters and 3x3 kernel size, ReLU activation
Max pooling layer with 2x2 pool size
Flatten layer
Dense layer with 128 nodes, ReLU activation
Output layer with 2 nodes, softmax activation
```

Some pitfalls to avoid when designing a CNN architecture are:

 - Choosing an overly complex architecture: It's important to strike a balance between having enough complexity to learn important properties of your data and avoiding overfitting. To avoid this pitfall, start with a simple architecture and gradually add complexity as needed.
- Not using enough training data: Deep learning models require large amounts of data to learn complex patterns in the data. Without enough data, the model may not generalize well to new data.
- Learning rate too high: A learning rate that is too high can cause the model to overshoot the optimal weights and degrade performance. It's important to experiment with different learning rates to find the best learning rate for your problem.
- Do not use regularization techniques: Regularization techniques such as dropout and L2 regularization help prevent overfitting and improve generalization performance of the model. It's important to try these techniques and see if they improve performance.
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