Why does one person downloading kill the internet for the rest of the house

Assuming full array of connection errors means partially loaded/infinitely loading web pages and/or packet loss:

In most countries DSLs are asymmetrical: your upload bandwidth is smaller (usually 10%) compared to your download bandwidth. What this means is that it's exponentially easier to saturate your uplink if there are no fully functional QoS systems in place to balance the connection and avoid saturation, specially if they don't take overhead data into calculation.

You could be facing two problems, maybe simultaneously: faulty QoS system(s) or bufferbloat. There are many layers where the bandwidth is managed and, consequently, problems could be introduced:

1. The end user application (e.g. a web browser or a P2P file sharing program).
2. A software firewall (usually part of security suites).
3. Your OS (On Windows 10 and 7, to check if the QoS service is activated go to ncpa.cpl > your adapter > properties > QoS Packet Scheduler).
4. Your router (you'll have to check the manual for your specific model, or the sticker under it, but you can usually access its configuration through your browser by going to the default gateway address, which is usually 192.168.1.1 but you can confirm with a 'ipconfig /all' on the command prompt).
5. Your modem, implying your modem and your router are separate devices (a correctly configured modem in this case should be on bridge mode and shouldn't apply any QoS rules, leaving it up to the router to manage the connection. Again, reach for a manual or ask online).
6. Your ISP. Many ISPs throttle torrent traffic but I have never heard of ISPs throttling downlink when uploading files. As another user commented, this probably isn't an issue with the ISP but if nothing else solves it you could give them a call.
7. The webserver (included just for completeness sake but probably unrelated to your issue, unless you were having exclusive problems browsing YouTube while uploading a video to it).

If a webserver can handle my device downlading multiple things from it at once, then why can't my device handle uploading multiple things to a webserver at once? How are the two any different?

Because the webserver that is providing you data is correctly configured to balance the output while your home network is failing on layers 1 to 5 above.

You'll have to troubleshoot as you haven't provided enough data to confirm where the problem is at. Here is my recommended process, assuming you have a router, a discrete modem and your internet connection is PPPoE:

Set-up:

1. Remove the router from your home network and connect your device directly to the modem with an Ethernet cable.
2. Make sure the modem is configured on 'bridge' mode. Additionally, check if the NAT, built-in firewall and the DHCP server are turned off.
3. Set up the PPPoE connection directly under your OS (this tutorial might interest you if you don't know how to do it).
4. Temporarily disable any software firewalls you might have installed (including the default one provided by Windows).

Try uploading something to YouTube again and see if the problem persists. If it doesn't, there's a problem with your firewalls or your router. You could try updating its firmware or flashing OpenWRT on it. If the problem persists, try those:

• Run this speedtest check from DSLReports. Note down your idle latencies and maximum download and upload speeds. While uploading and downloading, also write down your bufferfloat values. If your idle latencies are higher than 200ms, there's something wrong with your ISP or your home network. If your idle latencies are OK but the bufferfloat latencies are too high (way higher than 250ms) this confirms bandwidth saturation while transferring data, which can be fixed by limiting throughput on your applications and/or with adequate QoS packet scheduling systems.

• Try uploading large amounts of data somewhere else. Check if page loading still hangs. If it doesn't, there's something inherently wrong with your browser and/or with YouTube. If it does, you just need to find a way to limit your upload speed.

• I'm not aware of any YouTube settings or Firefox/Chrome extensions to limit your uplink, but you can try with an external program such as NetLimiter throttling Chrome's upload while browsing with another program such as Firefox. Set the upload limit to 60% of your upload bandwidth as measured on the DSLReports test above. Otherwise, run the test below:

• Download a torrent client such as Deluge. Unlimit the upload speed and force outgoing and incoming encryption. Randomize the connection port. Have a friend outside your LAN do the same. Grab a large file (e.g. a Linux distro .iso), make a .torrent and give it to your friend. Start uploading data to him and check if your upload speeds are constantly hitting your maximum uplink bandwidth as measured on the test above. Try browsing a page online, the problem should persist. Limit your upload speed to 60% of your maximum upload speed as measured on the test above. Try browsing a web page and see if the problem persists: it shouldn't. This just confirms the theory of bandwidth saturation if there is no management in place.

Report back your results.