How to prevent steam client from auto-updating itself?

This doesn't solve the steam update issue but hibernating your PC instead of shutting it down would bypass the problem and is almost as good as shutting down your PC if you're concerned by noise and/or power usage.

This works because hibernation saves the current running state of your PC to a file on the hard drive before shutting down. This file is then read back to RAM when you boot and your PC is restored to it's pre-hibernation state. Do still pause the download before hibernating to ensure steam properly finishes writing what it is currently downloading.

You might have to enable hibernation manually depending on your PC, windows, updates, etc. See this guide from Microsoft.

If it's actually updating and you're on the Steam Client Beta have you tried using the "stable" public version instead? It updates far less often, and should help minify any issues caused by client updates while you're downloading this game.

Most likely though you're not letting Steam shutdown properly before shutting down Windows or just closing the lid if it's a laptop, or you have a partially corrupt Steam client. If you don't care about the why/how you can skip the heading "Possible Fixes".

Steam doesn't constantly read/write it's configuration files. It may do so with some, but the core of it's config including the apps we have installed is loaded and changes made after that to the data on disk will be destroyed when it flushes the data back out to the disk. But, if it doesn't get to flush it back out because it's force closed or the machine is improperly shutdown it can cause problems ranging from it being left with the old data instead to plain ol' corruption, or worse data loss.

When starting Steam first validates much of the client's parts and configuration data through the Steam Client Bootstrapper. This is also the part that's responsible for installing updates to the client, and why it needs to restart to install updates. When corrupt parts/data are encountered it creates a .crash file in the Steam folder (wherever it's installed) which tells it to try to fix it on the next startup.

Then the bootstrapper restarts the client (which restarts itself too) and the "Checking for updates" .../... "Updating" window pops up and it will attempt to fix the existing data and start the client normally afterwards. This likely includes downloading fresh copies of some files, but I haven't watched while playing with the installed and downloaded parts directly to test it as of yet.

If Steam doesn't have write permission to access some of it's own files/folders when running as a user it can fail to save updated data. So, if you went playing with permissions in the Steam folder you may need to fully uninstall and then reinstall the client.

An overbearing anti-virus/anti-malware or other security program could cause this by blocking Steam from writing to some of it's own files. If you suspect this may be the case try whitelisting the bootstrapper and the client in them so they won't mess Steam up. Other non-security programs can also interfere with Steam.

A dying hard drive can cause corruption and data loss which can easily lead to issues like this. If this is the problem though most likely there would be other cases of corruption and data loss, not just the Steam client. If you suspect this may be the case you can try checking the SMART status of your drive on Windows using built-in tools (or smartmontools suggested right below that answer), and on Linux with smartmontools, or on Mac again smartmontools or just rely on Apple's Disk Utility app when it says "Verified" for SMART Status.