I think I found a bug in the 1.13.2 installer, in versions 25.0.87 and .89 at least, maybe earlier. I know it's Beta but this is just reporting, I'm not asking for help: I have a workaround as well, but I don't know if it really does work.

First off, i did search the forum for the error and got 0 results, and I don't know if there is somewhere else to look for known bugs.

I"m using Linux Mint 19.1

Clean install of Vanilla. Run 1.13.2 once and close.

Download and run forge-1.13.2-25.0.89-installer.jar. 

Select Client install. verify path and install.

Open Launcher (Being LInux this is the old 1.6.89-j launcher as the new launcher is not option.)

Select "forge" profile.  ---> The note above the Switch user button indicates still 1.13.2 .... NOT  the forge version as expected.

Click Edit profile.

Note that "Use Latest Release"  is selected and no forge version is available to chose from in the "Use Version" selection.

If I cancel the Edit profile window and click Play, Minecraft simply won't launch and no log file gets written

If I save the profile, then vanilla 1.13.2 is used (obviously since that was saved in the profile)

I tried editing the launcher_profiles.json to force a forge version but it just used Vanilla.

Launcher log shows an error:

Spoiler

[21:07:40 INFO]: Refreshing local version list...
[21:07:41 ERROR]: Couldn't load local version /home/chris/.minecraft/versions/1.13.2-forge-25.0.87/1.13.2-forge-25.0.87.json
com.google.gson.JsonSyntaxException: java.net.MalformedURLException: no protocol: 
    at com.google.gson.Gson.fromJson(Gson.java:818) ~[launcher.jar:1.6.89-j]
    at com.google.gson.Gson.fromJson(Gson.java:768) ~[launcher.jar:1.6.89-j]
    at com.google.gson.Gson.fromJson(Gson.java:717) ~[launcher.jar:1.6.89-j]
    at com.google.gson.Gson.fromJson(Gson.java:689) ~[launcher.jar:1.6.89-j]
    at net.minecraft.launcher.updater.LocalVersionList.refreshVersions(LocalVersionList.java:46) [launcher.jar:1.6.89-j]
    at net.minecraft.launcher.updater.MinecraftVersionManager.refreshVersions(MinecraftVersionManager.java:60) [launcher.jar:1.6.89-j]
    at net.minecraft.launcher.Launcher$2.run(Launcher.java:177) [launcher.jar:1.6.89-j]
    at java.base/java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:514) [?:?]
    at java.base/java.util.concurrent.FutureTask.run(FutureTask.java:264) [?:?]
    at java.base/java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1135) [?:?]
    at java.base/java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:635) [?:?]
    at java.base/java.lang.Thread.run(Thread.java:844) [?:?]
Caused by: java.net.MalformedURLException: no protocol: 
    at java.base/java.net.URL.<init>(URL.java:627) ~[?:?]
    at java.base/java.net.URL.<init>(URL.java:523) ~[?:?]
    at java.base/java.net.URL.<init>(URL.java:470) ~[?:?]
    at com.google.gson.internal.bind.TypeAdapters$18.read(TypeAdapters.java:448) ~[launcher.jar:1.6.89-j]
    at com.google.gson.internal.bind.TypeAdapters$18.read(TypeAdapters.java:440) ~[launcher.jar:1.6.89-j]
    at com.google.gson.internal.bind.ReflectiveTypeAdapterFactory$1.read(ReflectiveTypeAdapterFactory.java:93) ~[launcher.jar:1.6.89-j]
    at com.google.gson.internal.bind.ReflectiveTypeAdapterFactory$Adapter.read(ReflectiveTypeAdapterFactory.java:172) ~[launcher.jar:1.6.89-j]
    at com.google.gson.internal.bind.ReflectiveTypeAdapterFactory$1.read(ReflectiveTypeAdapterFactory.java:93) ~[launcher.jar:1.6.89-j]
    at com.google.gson.internal.bind.ReflectiveTypeAdapterFactory$Adapter.read(ReflectiveTypeAdapterFactory.java:172) ~[launcher.jar:1.6.89-j]
    at com.google.gson.internal.bind.ReflectiveTypeAdapterFactory$1.read(ReflectiveTypeAdapterFactory.java:93) ~[launcher.jar:1.6.89-j]
    at com.google.gson.internal.bind.ReflectiveTypeAdapterFactory$Adapter.read(ReflectiveTypeAdapterFactory.java:172) ~[launcher.jar:1.6.89-j]
    at com.google.gson.internal.bind.TypeAdapterRuntimeTypeWrapper.read(TypeAdapterRuntimeTypeWrapper.java:40) ~[launcher.jar:1.6.89-j]
    at com.google.gson.internal.bind.CollectionTypeAdapterFactory$Adapter.read(CollectionTypeAdapterFactory.java:81) ~[launcher.jar:1.6.89-j]
    at com.google.gson.internal.bind.CollectionTypeAdapterFactory$Adapter.read(CollectionTypeAdapterFactory.java:60) ~[launcher.jar:1.6.89-j]
    at com.google.gson.internal.bind.ReflectiveTypeAdapterFactory$1.read(ReflectiveTypeAdapterFactory.java:93) ~[launcher.jar:1.6.89-j]
    at com.google.gson.internal.bind.ReflectiveTypeAdapterFactory$Adapter.read(ReflectiveTypeAdapterFactory.java:172) ~[launcher.jar:1.6.89-j]
    at com.google.gson.Gson.fromJson(Gson.java:803) ~[launcher.jar:1.6.89-j]
    ... 11 more

Since it referred to 1.13.2-forge-25.0.87.json, I opened that up and found one entry that had a blank URL:

"libraries": [
        {
            "name": "net.minecraftforge:forge:1.13.2-25.0.89",
            "downloads": {
                "artifact": {
                    "path": "net/minecraftforge/forge/1.13.2-25.0.89/forge-1.13.2-25.0.89.jar",
                    "url": "",
                    "sha1": "e2f92a768141306c7e05c8130dd9d2ee4ada87c9",
                    "size": 147870
                }
            }
        },

 

 I removed that line ( "url": "", ), saved the file, and relaunched the launcher. I no longer got the error and it behaved as expected, launching Minecraft with forge installed.

What I don't know is whether removing the url from that entry is going to break anything else. It doesn't look like it, but I'm not the expert.

Use the updated launcher.