I'm going through your topics backwards...
What to read: You should read the book Programming Pearls by Jon Bentley. It's a really enjoyable and easy read, and even though you asked for articles, each chapter is an article he originally wrote for a magazine for programmers (I think Communications of the ACM but don't quote me) so you can read them separately. They're broadly about writing efficient programs. Along the way he gives some answers to why programming is affected by math, but don't think the whole point of the book is to convince you to love math, or to put up with math, or anything like that.
Programming and math: You don't have to solve equations to write programs. For our high school CS curriculum we specify Algebra 1 as a prerequisite, but only so that students will have seen the ideas of function and variable before. (In the very early days of computing, before they invented the idea of abstraction, programmers did sometimes have to solve equations because they had to work out exactly how many milliseconds it would take to carry out each instruction, in order to know where in memory to put the next instruction. But that was over long before I started programming.)
The kind of math that affects you as a programmer is stuff like understanding why mergesort is faster than insertion sort. And understanding why you're never going to write a program that can automatically debug all your other programs.
(By the way, if your plan is to be a web designer, you are setting your sights too low.)
What your parents and teachers say: So, here's the thing. If your father is really telling you that as a programmer you'll start every day by solving 20 equations as a warmup, that's not true. You don't need much school math to program. (Although, by the time you're looking for a job, most of them will be in Data Science, which does depend pretty heavily on statistics. Also, you guys like to talk about AI, and that also depends a lot on statistics these days.)
But programming is doing math, actual math, not school math. Math is about formal systems: reasoning from a small number of axioms using a small number of rules of inference. And a programming language is a formal system! The kind of reasoning you have to do in order to write and debug a program is exactly what mathematicians do.
How mathematicians are weird.
The thing that makes (pure) mathematicians different from the rest of us is how much they're willing to go meta. So a couple of sentences back I said math is about proving theorems from axioms. Well, what counts as a proof? How do we know a proof is valid? There's a branch of mathematics called proof theory in which proofs are the objects of analysis, and there are axioms and theorems about proving things. And if you're an applied mathematician, your job is to use math theory to model some actual real-world phenomena. Well, what does it mean for something to be a model of something else? That's the subject of model theory. And so on.
But part of what your father is saying is right: It's not that you have to do math because of the subject of some particular program you write. (Although if you want to be a game programmer, simulating physics is the least of your mathematical worries. Physics is easy. 3-D graphics is hard.) It's that writing a program is a mathematical activity, and if it's really math you hate, rather than school math, then yeah, you'll be banging your head against that no matter what your program is about.
What I want:
Yeah, I want you to tell me how many prime numbers there are! (No fair looking it up.)
About your essay, I think actually your problem in school may be that you like math too much. All those problems about doing computations with absolute values are there because some students need them! Because they don't really know what "absolute value" means. (Go back and read all the definitions y'all have posted in this thread, and try to figure out whether each person does or doesn't understand the idea.) By doing a lot of problems, with luck, they teach themselves. But you get it quickly and so the problems are a burden.
Talk your teacher into letting you skip the boring parts of the homework, by reading a chapter ahead and taking a unit test on the stuff the class hasn't learned yet.